Answer
$x=\frac{5}{4}$
Work Step by Step
Use the definition of the log function to solve for $x$. Rewrite the problem so that the base has the exponent of the opposite side and is equal to the log's number and/or variable. Then simplify the side with $x$ by factoring and then solving for $x$. The negative answer is not part of the domain.
$\log_5x+\log_5(4x-1)=1$
$\log_5x(4x-1)=1$
$5^1=x(4x-1)$
$5=4x^2-x$
$0=4x^2-x-5$
$0=(4x-5)(x+1)$
$4x-5=0$
$4x=5$
$x=\frac{5}{4}$
$x+1=0$
$x=-1$
