How do you solve $5^-x = 250$ ?

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Answer 1 · 2015-10-24T10:47:05

$x=-log_5(250)$

Since the logarithm is the inverse function of the exponential (i.e., $log_a(a^x)=x$ , you can use $log_5$ to isolate the $x$ :

$5^{-x}=250 \implies log_5(5^{-x})=log_5(250)$ ,

but $log_5(5^{-x})=-x$ .

So, the equation becomes $-x=log_5(250)$ , which we easily solve for $x$ changing the sign.

How do you solve 5^-x = 2505^-x = 250?