Answer
$5^{-2x}=40$
$\log_{5}40=-2x$
$\frac{\log_{5}40}{-2}=x$
$\frac{2.2920}{-2}=x$
$-1.1460=x$
Work Step by Step
The definition of the logarithm function can be translated into mathematical formulas such as the following. The given expressions are equivalent.
The exponential form: $b^{x}=a$
The logarithmic form: $\log_{b}a=x$.
The given equation can be solved with the logarithmic form, therefore we shall transform it:
$5^{-2x}=40$
$\log_{5}40=-2x$
$\frac{\log_{5}40}{-2}=x$
$\frac{2.2920}{-2}=x$
$-1.1460=x$
