# How do you solve the exponential equation #2^(x+2)=16^x#?

##### 2 Answers

Feb 17, 2017

#### Explanation:

Note that

#16=2^4#

#rArr2^(x+2)=(2^4)^x#

#rArrcolor(red)(2)^(x+2)=color(red)(2)^(4x)# Since the bases are equal, that is

#color(red)(2)# then the exponents are equal.

#"solve "4x=x+2#

#rArr3x=2#

#rArrx=2/3" is the solution"#

Feb 17, 2017

#### Explanation:

because the base on the LHS =2 and base on RHS=2,

so the exponents are equal

multiply both sides by

substitute