Properties of Logarithms

Two different cars each depreciate to 60% of their respective original values. The first car depreciates at an annual rate of 10%. The second car depreciates at an annual rate of 15%. What is the approximate difference in the ages of the two cars?

1.7 years

Which of the following shows the extraneous solution to the logarithmic equation below?

A. x=-6

One brand of vinegar has a pH of 4.5. Another brand has a pH of 5.0. The equation for the pH of a substance is pH = -log[H+], where H+ is the concentration of hydrogen ions. What is the approximate difference in the concentration of hydrogen ions between the two brands of vinegar?

A. 2.2*10^-5

An equation for the depreciation of a car is given by y = A(1 - r)t, where y = current value of the car, A = original cost, r = rate of depreciation, and t = time, in years. The current value of a car is $12,282.50. The car originally cost $20,000 and depreciates at a rate of 15% per year. How old is the car?

C. 3 years

What are the domain and range of mc017-1

B. domain: x > 1; range: all real numbers

Given log(3^2)= 0.631 and log(3^7)= 1.771, what is log(3^14)?

c. 2.402

Which expression is equivalent to logw (x^2 -6)^4 / 3√x^2 + 8) ?

c. 4logw(x^2 -6) - 1/3 logw(x^2 + 8)

Given log4(3) = 0.792 and log4(21) = 2.196 what is log4(7)?

a. 1.404

Which of the following is equivalent to log (1/9)/k?

a. log1/9 -logk

Which of the following is equivalent to log9w?

a. log9 + logw

Which is the graph of y=-log(x-2)+3

D

Which expression is equivalent to log18 - log(p + 2)?

b. log 18/p+2

Which expression is equivalent to log6(4a) (b-4/c^4)?

b. log8(4) + log8(a) +(log8(b-4)-4log8c)

Which expression is equivalent to logc (x^2 - 1)/5x ?

c. logc (x^2 - 1)-(logc5 + logcx)

What is rewritten using the power property?

B. floge

What is written as a single logarithm?

B. log base 1/2 w^4 (u^2/v^3)

For what values of x does

B. x=-3, x=1

Which expression is equivalent to log12 (1/2 / 8w)?

b. log(12^1/2) - (log12^8 + 12w)

Which expression is equivalent to log(8^4a) (b-4)/c^4)?

b. log(8^4) + log(8^4) + log(8(b-4)-4log(8^c)

What is 2(log(3^8)+ log3(3^4 - 7^2)) written as a single logarithm?

b. log3(2z^2)

What is 2log5(5x^3) + 1/3 log5 (x^2 + 6) written as a single logarithm?

b. log5(25x^6)3√x^2 + 6

Which expression is equivalent to log3(x + 4)?

c. log3 + log(x + 4)

Which expression is equivalent to log3 (c/9)?

c. log3 c - log3(9)

The two expressions below have the same value when rounded to the nearest hundredth. What is the approximate value of to the nearest hundredth?

B. 1.23

If , what is the value of x?

B. 8/5

What is the range of the function f(x) = -2(6x) + 3?

B. - infinity, 3

What is the solution of logx729=3

B. 9

What is log15(2^3) rewritten using the power property?

d. 3log(15^2)

The loudness, L, measured in decibels (Db), of a sound intensity, I, measured in watts per square meter, is defined as L= 10log I/I(0), where I(0) = 10^-12 and is the least intense sound a human ear can hear. What is the approximate loudness of the dinner conversation, with a sound intensity of 10-7, Rajah has with his parents?

d. 50 Db

What is log5(4 * 7) + log(5^2) written as a single log?

d. log(5^56)

A student showed the steps below while solving the equation by graphing. Step 1: Write a system of equations: Step 2: Use the change of base formula to rewrite the equations: Step 3: Graph the two equations: In which step did the student make the first error?

step 2

Which of the following shows the graph of y = -(2)x - 1?

B