log question

logbase4(15) = x

by definition of logs     15 = 4^x

take log base 10 of both sides

log 15 = log(4^x)

log 15 = x log 4

x = log 15/log 4  = 1.95344 ~ 1.953

Use base change formula.

$\log_415 = x\\ x = \dfrac{\ln 15}{\ln 4} \approx 1.953$