(02/24) ALG 2 Solving Exponential Equations

(02/24) ALG 2 Solving Exponential Equations

Multiple Choice

Rewrite as a log:

 $8^x=12$  

•  $\log_8x=12$  

•  $\log_{12}8=x$  

•  $\log_812=x$  

•  $\log_x12=8$  

Multiple Choice

Rewrite the logarithmic equation. $\log_3y=4$  

•  $4^y=3$  

•  $4^3=y$  

•  $3^4=y$  

•  $y^4=3$  

 $Step\ One\rightarrow8^x-37+37=-12+37\ \left(Add\ 37\ to\ both\ sides\right)$  
  $8^x=25$  

Solve: 
 $8^x-37=-12$  

• Step 1: Isolate the base & exponent by adding 37 to both sides  $8^x-37+37=-12+37\$  

•  $8^x=25$  

• Step 2: Rewrite as a log function  $\log_825=x$  

• Step 3: Solve for x by using the change of base formula. ** Use your calculator!!

•  $\left(\frac{\log\ \left(25\right)}{\log\ \left(8\right)}\right)=x$  

•  $x\ =\ 1.548\ \left(Final\ Answer\right)$  

Solve:  $4^{x-2}+14=21$  

•  $4^{x-2}+14-14=21-14$  

•  $4^{x-2}=7$  

•  $\log_4\left(7\right)=x-2$  

•  $\log_4\left(7\right)+2=x-2+2$  

•  $\log_4\left(7\right)+2=x$  

• ** Use calculator to solve!!

•  $\left(\frac{\log7}{\log\ 4}\right)+2=x$                              $x=3.404$  

Solve:   $3e^x-37=20$  

•  $3e^x-37+37=20+37$  

•  $3e^x=57$  

•  $\frac{3e^x}{3}=\frac{57}{3}$  

•  $e^x=19$  

•  $\ln\ \left(19\right)=x\ \ \ \ \ \ \ \left(Rewrite\ as\ natural\ \log u\sin g\ \ln\right)$  

• Place  $\ln\left(19\right)$  in your calculator to solve!!

•  $x=2.944$  

Multiple Choice

Solve for x:

9^x+8 = 81

• 2

• -6

• 6

• 8

Multiple Choice

Solve for x:

9^x+8 = 81

• 2

• -6

• 6

• 8

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