Question

0.2^x= 25
Solve to find x
Show steps

Answer 1

You said 0.2^x = 25

Take the logarithm of each side: x log(0.2) = log(25)

Divide each side by log(0.2): x = log(25) / log(0.2)

= 1.39794 / -0.69897 = -2

Answer 2

`0.2=(2)/(10)=(1)/(5)=5^(-1)\ \ \ |used\ a^(-1)=(1)/(a)\ for\ a\\eq0\\\\25=5^2\\\\therefore\\\\0.2^x=25\to(5^(-1))^x=5^2\ \ \ |use\ (a^n)^m=a^(n\cdot m)\\\\5^(-1(x))=5^2\\\\5^(-x)=5^2\iff-x=2\to\boxed{x=-2}\\\\check:\\\\0.2^x=0.2^(-2)=\left((1)/(5)\right)^(-2)=5^2=25\ O.K.\ :)`