Solve: log₂(3x) × log₅(8) = log₅(a) + log₅(2a) for Variable X

Question

$\log_23x\times\log_58=\log_5a+\log_52a$

Given a>0 , express X by a

00:00 Express X in terms of A

00:07 Use the logarithm product formula, switch between bases

00:22 Calculate the logarithm

00:32 Substitute the solution and continue solving

00:47 Use the formula for logarithm of a power

00:57 Compare the numbers

01:07 Isolate X

01:22 And this is the solution to the question

$\sqrt[3]{\frac{2a^2}{27}}$