Proof for the Power Rule

log_a xⁿ = nlog_a x

Proof:

Step 1: 
Let m = log_a x

Step 2: Write in exponent form 
x = a^m

Step 3: Raise both sides to the power of n
xⁿ = ( a^m )ⁿ

Step 4: Take log _a of both sides and evaluate 
log _a xⁿ = log _a a^mn
log _a xⁿ = mn log _a a
log _a xⁿ = mn
log _a xⁿ = n log_a x

SOURCE:

http://www.onlinemathlearning.com/logarithms-properties.html

Even a video on this 1: