solve In(4x)=Ig 3 x Ig 5

what's ln vs lg?

Assuming all logs are the same, and taking powers of e,

e^(ln 4x) = e^(ln3 * ln5) (e^ln3)^(ln5)
4x = 3^(ln5)
x = 1/4 * 3^(ln5) = 1.46

If the logs are different bases, then adjust the powers accordingly