## College Algebra (11th Edition)

$x=-5$
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.