Log(base(x))x^(m-1) +1=m

I don't know how I'm supposed to prove this

log x x^(m-1) + 1 = m

LS = log x x^(m-1) + 1
= (m-1)log x x + 1 , (using the rule log a^n = nloga)
= (m-1)(1) + 1 , since log n n = 1
= m-1 + 1
= m
= RS