(02/24) ALG 2 Solving Exponential Equations

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!!

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

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

 $4^{x-2}+14-14=21-14$  

 $4^{x-2}=7$  

 $\log_4\left(7\right)=x-2$  

 $\log_4\left(7\right)+2=x-2+2$  

 $\log_4\left(7\right)+2=x$  

** Use calculator to solve!!

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

 $3e^x-37+37=20+37$  

 $3e^x=57$  

 $\frac{3e^x}{3}=\frac{57}{3}$  

 $e^x=19$  

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

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

 $x=2.944$  

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