Using Properties to Solve Exponential Equations

Using Properties to Solve Exponential Equations

Fill in the Blanks

What exponent makes this equation true?

 $8^x=64$  

Fill in the Blanks

What exponent makes this equation true?

 $3^x=27$  

Fill in the Blanks

What exponent makes this equation true?

 $4^x=4^5$  

Fill in the Blanks

Solve for x:

 $\left(2\right)^x=8$  

Multiple Choice

How do you isolate the exponential part?

• Divide both sides by 4

• Multiply both sides by 4

• Divide both sides by 5

Fill in the Blanks

Now let's solve for x:

 $5^x=25$  

Multiple Choice

Let's practice some more.

 $2\left(3\right)^k=162$  
First we have to ____________

• isolate the exponential 

• multiply 2 and 3

Fill in the Blanks

First, isolate the exponential part by dividing both sides by 2

Then, find the value of k

 $2\left(3\right)^k=162$  

Multiple Choice

How do we isolate the exponential part in this equation?

 $\frac{1}{2}\left(7\right)^x=171.5$  

• Divide both sides by 2

• Multiply both sides by 2

Fill in the Blanks

When we multiply both sides by 2 we get  $7^x=343$  

What is the value of x?

Poll

Which would you rather do to isolate the exponential in the equation

 $\frac{2}{3}\left(3\right)^x=18$ ? 

• multiply both sides by the reciprocal of 2/3

• multiply both sides by 3, then divide both sides by 2

Fill in the Blanks

We get the same answer either way:

 $\left(3\right)^x=27$  
Now let's find the value of x

Fill in the Blanks

Solve for t:

 $\frac{2}{5}\left(5\right)^t=250$