Topic 14 Test Review

Topic 14 Test Review

Exponetial and Log Review

Multiple Choice

The inverse of an exponential function is a...

• absolute value function

• quadratic function

• logarithmic function

• square root function

Multiple Choice

What is the base of the  $\ln$  ?

• 10

• b

• e

• g

Multiple Choice

What is the base of the common log?

Ex:  $\log\left(5x\right)$  

• e

• 10

• 5

• g

Logarithmic Properties Review

Multiple Choice

To expand a logarithmic expression, you would...

• write the word 'log' as many times as the number of parts needed.

• write the word 'log' only one, single time.

Multiple Choice

To condense a logarithmic expression, you would...

• write the word 'log' only one, single time.

• write the word 'log' for as many times as the number of parts needed.

Multiple Choice

The Power Rule

The power moves to the...

• denominator

• back

• fraction

• front

Solving Logarithmic Equations Review

A logarithmic equation is an equation containing a variable in a logarithmic expression.

Example:  $\log_4\left(x+3\right)=2$  

2 Methods to Solve Log Equations

• Definition of a Log

• Example:  $\log_2\left(2x+7\right)=8$  

• One-to-One Property

• Example:  $\log_7\left(8x+8\right)=\log_7\left(9x\right)$  

Multiple Choice

What is the first step you would take to solve this log equation?

 $\ln\left(2x\right)=\ln\left(5x+8\right)$  

• Subtract one of the logs

• Set  $2x=5x+8$  

• Divide one of the logs

• Added 'e' as a base

Multiple Choice

What is the first step you would take to solve this log equation?

 $\log_32x=4$  

• Subtract 4

• Convert to exponential

• Subtract  $\log_32x=4$  

• Divide by  $2x$  

Solving Exponential Equations Review

An exponential equation is an equation that includes a variable in an exponent.

Example:  $2^{3x}=8$  

Powers of the Same Base Method

• Express each side as a power of the same base.

• Set the powers equal to each other and solve for your variable.

Multiple Choice

Does the Powers of the Same Base method work every single time?

• No

• Yes

Use Logs to Solve Exponentials

• Isolate the exponential expression

• Take the log of each side

• Simplify

• Solve for your variable

Great Job!

Let's move on to the second part of our review!