Answer
$x=-5$
Work Step by Step
Using the Product Property of logarithms, the given expression, $
\log(x+25)=\log(x+10)+\log4
$ is equivalent to
\begin{array}{l}\require{cancel}
\log(x+25)=\log[4(x+10)]
.\end{array}
Since the bases of the logarithms are the same, then these can be dropped. Hence,
\begin{array}{l}\require{cancel}
x+25=4(x+10)
.\end{array}
Using the properties of equality, the solution to the equation above is
\begin{array}{l}\require{cancel}
x+25=4x+40
\\\\
x-4x=40-25
\\\\
-3x=15
\\\\
x=\dfrac{15}{-3}
\\\\
x=-5
.\end{array}
Upon checking, $
x=-5
$ satisfies the original equation.
