# Logarithms and Exponential Functions

Logarithmic Functions

# At a Glance - Logarithmic Functions

You get a message dropped through a crack in your window in the middle of the night. It reads, "I am ready to lend a hand in the fight against the evil Expo. Meet me in the park at noon tomorrow." When you get there the next day, it's none other than Ms. Log Arithm! She greets you warmly and jumps right to business.

#### Example 1

 Solve the exponential equation 3x – 5 = 15y + 5 for x.

#### Example 2

 Change log4 20 to base-10 and solve to four decimal places.

#### Example 3

 Find the inverse of y = (7x + 5)1/5.

#### Example 4

 Show to three decimal places that log4 64 = log7 343 using base-10 logarithms.

#### Exercise 1

Solve the following exponential equation for y:

7(y + 1) = 3x + 3

#### Exercise 2

Find x in the following exponential equation. Do not simplify to decimals:

4ex + 10 = 20

#### Exercise 3

What value of x satisfies the following equation?

log10 10 = x

#### Exercise 4

What value of x satisfies the following equation?

log3 1 = x

#### Exercise 5

Is the following logarithmic equation valid for any one value of x?

log10 x = -3

#### Exercise 6

Solve the following exponential equation for y:

e(y + 4) – 15 = x2

#### Exercise 7

Solve the logarithmic equation  for x. Do not simplify to decimals.

#### Exercise 8

Evaluate the following log equation for x = 9:

y = log3(x2)

#### Exercise 9

Evaluate the following log equation for x = 5, to three decimal places:

y = ln(3x) + ln(ex)

#### Exercise 10

Evaluate the following log equation to three decimal places using only base-10 logarithmic functions:

y = log3 13

#### Exercise 11

Write log4 17 in base-10 form.

#### Exercise 12

Write ln(4x) in base-10 form.