Exponential and Logarithmic Functions and Applications *Review*

Bonus- Solve for extraneous solutions. ln(x-2)+ln(2x-3) = 2lnx

1= Extraneous Solution 6= Only Solution

A total of $9000 is invested at an annual interest rate of 2.5%, compounded annually. Find the balance in the account after 5 years

Balance in the account after 5 years will be about $10,182.67 .

Bonus- Double Your Investment You have deposited $500 in an account that pays 6.75% interest, compounded continuously. How long will it take your money to double?

It will take 10.27 years --> 10 years

A total of $12,000 is invested at an annual interest rate of 3%. Find the balance after 4 years for each type of compounding. Find quarterly and continuous.

Quarterly= $13,523.91 Continuous= $13,529.96

What is the Natural Base e?

The base of a logarithmic function of an irrational number (e).

What is an exponential function?

The exponential function f with base a is denoted by f(x) = a^x a > 0 , x is a real number

What is a logarithmic Function?

The function given by f(x) = log(a)x Logarithmic function with base a.

Solve the exponential Equations. a.eⁿ=72 b.3(2ⁿ) = 42

a. 4.28 b. 3.81

Use the properties of Logarithms to solve the following. a. ln6 b. ln2/27

a. ln6 = ln2 +ln3 b. ln2 - 3ln3

Use the properties of logarithms to expand each expression. a. log4(5x³y) b. ln(√3x-5/7)

a. log4(5)+3log4(x)+log4(y) b. 1/2ln(3x-5) - ln7

Evaluate the function f(n) = eⁿ (-2) (.25) (-0.4) (2/3) *Round to the nearest hundreth)

f(-2)=.14 f(.25)=1.28 f(-.04)=.67 f(2/3)=1.95

Evaluate the function f(x)=log10 (x) x=10 x=2.5 x=-2 x=1/4 *Round to the nearest hundredth*

f(10)=1 f(2.5)=.398 f(-2)= DNE f(1/4)= -.602

Evaluate each logarithm with the indicated value of x. f(x)=log2(x) x=32 f(x)=log3(x) x=1 f(x)=log4(x) x= 2 f(x)=log10(x) x= 1/100

f(32)= 5 f(1)= 0 f(2)= 1/2 f(1/100) = -2

Bonus Exponential Equation 4e(2x)-3 = 2

x= .11

Bonus Logarithmic Equation log3(5x-1) = log3(x+7)

x=2