#### Answer

$x=-2$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
To solve the given equation, $
x=\log_{4/5} \dfrac{25}{16}
,$ use the properties of logarithms.
$\bf{\text{Solution Details:}}$
Using exponents, the equation above is equivalent to
\begin{array}{l}\require{cancel}
x=\log_{4/5} \dfrac{5^2}{4^2}
.\end{array}
Using the Negative Exponent Rule of the laws of exponents which states that $x^{-m}=\dfrac{1}{x^m}$ or $\dfrac{1}{x^{-m}}=x^m,$ the equation above is equivalent to
\begin{array}{l}\require{cancel}
x=\log_{4/5} \dfrac{4^{-2}}{5^{-2}}
.\end{array}
Using the extended Power Rule of the laws of exponents which states that $\left( \dfrac{x^my^n}{z^p} \right)^q=\dfrac{x^{mq}y^{nq}}{z^{pq}},$ the equation above is equivalent to
\begin{array}{l}\require{cancel}
x=\log_{4/5} \left(\dfrac{4}{5}\right)^{-2}
.\end{array}
Using the Power Rule of Logarithms, which is given by $\log_b x^y=y\log_bx,$ the equation above is equivalent
\begin{array}{l}\require{cancel}
x=-2\log_{4/5} \dfrac{4}{5}
.\end{array}
Since $\log_b b =1,$ the equation above is equivalent to
\begin{array}{l}\require{cancel}
x=-2(1)
\\\\
x=-2
.\end{array}