# How do you solve #8=(1/4)^x#?

##### 1 Answer

May 20, 2018

#### Explanation:

#"using the "color(blue)"laws of exponents"#

#•color(white)(x)a^mhArr1/a^m" and "(a^m)^n=a^(mn)#

#"left side "=8=2^3#

#"right side "=(1/4)^x=(1/2^2)^x=(2^-2)^x=2^((-2x))#

#rArr2^3=2^(-2x)larrcolor(blue)"equating both sides"#

#"since the bases on both sides are 2 equate the exponents"#

#rArr-2x=3rArrx=-3/2#