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

1 Answer
May 20, 2018

x=-3/2

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