Answer
$t=\dfrac{\log5}{10\log1.375}\approx0.505391$
Work Step by Step
$10(1.375)^{10t}=50$
Take the factor $10$ to divide the right side of the equation:
$1.375^{10t}=\dfrac{50}{10}$
$1.375^{10t}=5$
Apply $\log$ to both sides of the equation:
$\log1.375^{10t}=\log5$
Using the power of a power rule, the left side of the equation can be rewritten like this:
$\log(1.375^{10})^{t}=\log5$
Take down the exponent $t$ to multiply in front of the $\log$:
$t\log(1.375)^{10}=\log5$
Solve for $t$:
$t=\dfrac{\log5}{\log(1.375)^{10}}=\dfrac{\log5}{10\log1.375}\approx0.505391$
