Unit 2 Practice

Use the properties of logarithms to expand the expression: log 4^(2xy^2) Expanded expression:?

Properties of Logarithms: 1- log b^(c*d) = log b^(c) + log b^(d) 2- log b^(c/d) = log b^(c) - log b^(d) 3- log b^(c)^r = r*log b^(c) To expand this expression as much as possible, we swill start with property 1. Log 4^(2xy^2); in the parenthesis 2x will be c, and y^2 will be d. So we have log 4^(2x)+log 4^y^2). We want to expand these as much as possible, and the first log log 4^(2x) can be expanded by again using property 1. So now we have log 4^(2)+log 4^(x)+log4^(y^2). This last log can be expanded by using property 3. log 4^(y^2)= 2*log 4^(y). Now that we have expanded this expression as much as possible, we are done. The answer is: log 4^(2)+log 4^(x)+2*log 4^(y)

Evaluate the following logarithm: Log 3^3^5=x x=?

To solve for x, convert logarithm function to exponential form. Log 3^3^5 -> 3^x=3^5. This gives you the answer: x=5

How much money will there be in an account at the end of 10 years if $3000 is deposited at 6% annual interest compounded annually: (Assume no withdrawals are made.) Round your answer to the nearest cent Money in account:?

Formula: A=p(1+r/n)^n*t p=$3,000 r=6% -> .06 n=1 t=10 A=3,000(1+0.06/1)^10 = 5,372.54309 Answer: $5,372.54

How much money will there be in an account at the end of 10 years if $3000 is deposited at 6% annual interest compounded daily: (Assume no withdrawals are made.) Round your answer to the nearest cent Money in account:?

Formula: A=p(1+r/n)^n*t p=$3,000 r=6% -> .06 n=365 t=10 A=3,000(1+0.06/365)^(365*10) A=3,000(1.000164384)^3650=5466.086834 Answer: $5,466.09

How much money will there be in an account at the end of 15 years if $4000 is deposited at 2% annual interest compounded twice annually: (Assume no withdrawals are made.) Round your answer to the nearest cent Money in account:?

Formula: A=p(1+r/n)^n*t p=$4,000 r=2% -> .02 n=2 t=15 A=4,000(1+0.02/2)^(2*15) A=4,000(1.01)^30= 5,391.395661 Answer: $5,391.40

Use the properties of logarithms to expand the expression: log 2^(2x^2/y) Expanded expression:?

Properties of Logarithms: 1- log b^(c*d) = log b^(c) + log b^(d) 2- log b^(c/d) = log b^(c) - log b^(d) 3- log b^(c)^r = r*log b^(c) First, start expanding the expression with property 2. log 2^(2x^2)-log 2^(y). Now use property 1 to expand the first logarithm. log 2^(2)+log 2^(x^2)-log 2^(y). Finally, use property to expand the second logarithm. This will complete the expansion. The answer is: log 2^(2)+2*log 2^(x)-log 2^(y)

Use the properties of logarithms to expand the expression: log (x^2 sqrt y/z) Expanded expression:?

Properties of Logarithms: 1- log b^(c*d) = log b^(c) + log b^(d) 2- log b^(c/d) = log b^(c) - log b^(d) 3- log b^(c)^r = r*log b^(c) To expand this expression, we first have to get rid of the sqrt y. (Hint: to get rid of a square root, you can instead write y ^1/2.) Now that we've gotten rid of the square root, the expression looks like this: log (x^2 y^(1/2)/z. The first property to use would be the second. So, now the expression is log(x^2 y^1/2)-log(z). Next we use property 1 to expand the first logarithm. Log(x^2)+log(y^1/2)-log(z). Now we want to expand those logarithms further by sing property 3. This will completely expand the expression; the answer is: 2*log(x)+1/2*log(y)-log(z)

Express the exponential equation as a logarithm: 3e^4x=9 Logarithmic function:?

To change this exponential function into a logarithm, we first divide both sides by 3. This will leave us with e^4x=3. Now we can take the natural log (ln) of both sides. This will allow us to cancel out the e, and bring the exponents down. Now we have the answer: 4x=ln3

Express the exponential equation as a logarithm: 4e^2x=8 Logarithmic function:?

To change this exponential function into a logarithm, we first divide both sides by 4. This will leave us with e^2x=8. Now we can take the natural log (ln) of both sides. This will allow us to cancel out the e, and bring the exponents down. Now we have the answer: 2x=ln8

Express the exponential equation as a logarithm: 5e^5x=15 Logarithmic function:?

To change this exponential function into a logarithm, we first divide both sides by 5. This will leave us with e^5x=3. Now we can take the natural log (ln) of both sides. This will allow us to cancel out the e, and bring the exponents down. That gives us the answer: 5x=ln3

Solve for t, and express the solution as a logarithm: 4^2t=6 t=?

To solve for t, try converting the expression to logarithm form. 4^2t=6 -> log4^6=2t. This doesn't give us the right answer because we need to isolate the t. So, convert back to exponential form, and simplify the base. we know that 4=2^2; so now the expression is (2^2)^2t=6 Simplify further by multiplying the exponents. Now we have 2^4t=6 converting this into a logarithm gives you log 2^6=4t. divide both sides by 4 to isolate the t. The answer is: t= 1/4log2^6

Solve for t, and express the solution as a logarithm: 8^4t=16 t=?

To solve for t, try converting the expression to logarithm form. 8^4t=16 -> log 8^16=4t. This doesn't give us the right answer because we need to isolate the t. So, convert back to exponential form, and simplify the base. we know that 8=2^3; so now the expression is (2^3)^4t=16 Simplify further by multiplying the exponents. Now we have 2^12t=16 converting this into a logarithm gives you log 2^16=12t. divide both sides by 12 to isolate the t. The answer is: t= 1/12log2^16

Use your calculator and the definition of logx (recall: the base is 10) to find the value of x. logx=0 x=?

To solve for x, convert from logarithmic to exponential form. log 10^x=0 -> 10^0=x. Use your calculator to find the value of 10^0=1. The answer is: x=1

Use your calculator and the definition of logx (recall: the base is 10) to find the value of x. logx=1 x=?

To solve for x, convert from logarithmic to exponential form. log 10^x=1 -> 10^1=x. Use your calculator to find the value of 10^1=10. The answer is: x=10

Use your calculator and the definition of logx (recall: the base is 10) to find the value of x. (Round your answers to 4 decimals.) logx=1/2 x=?

To solve for x, convert from logarithmic to exponential form. log 10^x=1/2 -> 10^1/2=x. Use your calculator to find the value of 10^1/2=3.16227766. Round to four decimals; The answer is: x=3.1623

Use your calculator and the definition of logx (recall: the base is 10) to find the value of x. (Round your answers to 4 decimals.) logx=1/4 x=?

To solve for x, convert from logarithmic to exponential form. log 10^x=1/4 -> 10^1/4=x. Use your calculator to find the value of 10^1/4=1.77827941. Round to 4 decimals; The answer is: x=1.7783

Evaluate the following logarithm: Log10=x x=?

To solve for x, convert logarithm function to exponential form. (Hint: if there is no visible base, the base is 10.) Log 10^10 -> 10^x= 10. Now, all you have to do is figure out to which power you have to raise 10 to get 10. Answer: x=1

Solve for x: Log 5^25=x x=?

To solve for x, convert logarithm function to exponential form. Log 5^25 -> 5^x=25. Now, all you have to do is figure out to which power you have to raise 5 to get 25. The answer is: 5^2=25 x=2

Solve for x: Log 72^1=x x=?

To solve for x, convert logarithm function to exponential form. Log 72^1 -> 72^x=1. Now, all you have to do is figure out to which power you have to raise 72 to get 1. The answer is: 72^0=1 x=0

Solve for x: Log 8^512=x x=?

To solve for x, convert logarithm function to exponential form. Log 8^512 -> 8^x=512. Now, all you have to do is figure out to which power you have to raise 8 to get 512. The answer is: 8^3=512 x=3

Solve the exponential equations using logarithms and your calculator. Round your answer 2 decimal places. 10^n=483.059 n=?

To solve this equation, take the log of both sides. This will allow you bring down the exponents. log 10^(10^n)=log 10^(483.059). Enter into your calculator log 10^(483.059); that answer will be 2.68400018. Round your answer to two decimal places. The answer will be: n=2.68

Solve the exponential equations using logarithms and your calculator. Round your answer 2 decimal places. 15^n=28.3064 n=?

To solve this equation, take the log of both sides. This will allow you bring down the exponents. log 10^(15^n)=log 10^(28.3064). Enter into your calculator log 10^(28.3064); that answer will be 1.2345. Round your answer to two decimal places. The answer will be: n=1.24

Solve for x: (1/4)^x=16 x=?

To solve this problem, make both sides of the equal sign have the same base. We know that 16=4^2. We want both sides to have the same base though, so we switch the denominator, which mean 4^2= 1/4^-2= (1/4)^-2. Now the equation is (1/4)^x=(1/4)^-2. That's our answer: x=-2

Solve for x: 3^(10-x)=27 x=?

To solve this problem, make both sides of the equal sign have the same base. We know that 3^3=27, so 3^(10-x)=3^3. Now that the bases are the same, we can cancel them out; 10-x=3. Add x to both sides; 10=3+x. Subtract 3 from each sides, and the answer is: x=7

Solve for x: 3^(x+4)=243 x=?

To solve this problem, make both sides of the equal sign have the same base. We know that 3^5=243, so 3^(x+4)=3^5. Now that the bases are the same, we can cancel them out; x+4=5. Subtract 4 from both sides, and that gives the answer: x=1

Use the given values and the properties of logarithms to find the indicated logarithm. Given: log 16≈1.2 log 5≈0.7 log 8≈0.9 Find log(5/8)≈?

log 16≈1.2 log 5≈0.7 log 8≈0.9 To find the value of log(5/8), first expand the log using the logarithm expanding property 2. This will give you log(5)-log(8). The given values above indicate log 5≈0.7, and log 8≈0.9; so log 5-log 8 = 0.7-0.9=-0.2 The answer is: log(5/8)≈-0.2

Use the given values and the properties of logarithms to find the indicated logarithm. Given: log 3^2≈0.6 log 3^5≈1.5 Find log 3^(8/15)≈?

log 3^2≈0.6 log 3^5≈1.5 To find the value of log 3^(8/15), first expand the log using the logarithm expanding property 2. This will give you log 3^8-log 3^15. Since neither of these values are given, simplify the logs. We know that 8=2^3, and 15=3*5. So now the logarithm is: log 3^(2^3)-log 3^(3*5). We can expand that to 3*log 3^2-(log 3^3+log 3^5). Now we just insert the decimal values. 3*log 3^2= 0.6*3=1.8; log 3^3=1 log 3^5=1.5; 1.8-(1+1.5)=-0.7 Answer: log 3^(8/15)≈-0.7