6.5 Solving Exponential Equations

Solve the following exponential equation:
 $9^{8-x}=27^{x-3}$  

•  $x=5$  

•  $x=-5$  

•  $x=\frac{1}{5}$  

•  $x=-\frac{1}{5}$  

Solve the following exponential equation:

 $7^{-x}=49$  

•  $x=1$  

•  $x=-1$  

•  $x=2$  

•  $x=-2$  

Solve the following exponential equation:
 $2^x=4^{x+1}$  

•  $x=-2$  

•  $x=2$  

•  $x=-3$  

•  $x=3$  

Solve the following exponential equation:
 $5^{-3x}=125$  

•  $x=-1$  

•  $x=-4$  

•  $x=-3$  

•  $x=1$  

Tags

CCSS.HSF.BF.B.5

Solve the following exponential equation:

 $3^3=3^{4x+2}$  

•  $x=\frac{1}{4}$  

•  $x=-\frac{1}{4}$  

•  $x=\frac{1}{2}$  

•  $x=-\frac{1}{2}$  

Solve the following exponential equation:
 $4^{p+2}=64$  

•  $p=-1$  

•  $p=1$  

•  $p=\frac{1}{2}$  

•  $p=\frac{7}{6}$  

How would you solve an exponential equation like the one below:

 $36=6^x$  

• Rewrite  $36$  as  $6^2$  

• Set the exponents equal to each other

• Rewrite  $36$  as  $6^3$  

• Multiply the exponents

Solve the following exponential equation:
 $8=2^{5x+7}$  

•  $x=\frac{4}{5}$  

•  $x=\frac{1}{4}$  

•  $x=-\frac{4}{5}$  

•  $x=-\frac{1}{4}$  

Solve the following exponential equation:
 $2^{3n}=4$  

•  $n=2$  

•  $n=3$  

•  $n=\frac{2}{3}$  

•  $n=4$  

Solve the following exponential equation:

 $2^{-m}=2^{3m-3}$  

•  $m=\frac{4}{3}$  

•  $m=\frac{3}{4}$  

•  $m=-\frac{4}{3}$  

•  $m=-\frac{3}{4}$