Question 1209209
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Log Rules
log(M*N) = log(M)+log(N)
log(M^N) = N*log(M)
Let's refer to these as equations (1) and (2)


{{{x = 2^a}}} converts to the log form {{{log(2,(x)) = a}}}
I'll refer to this as equation (3)


Also,
{{{y = 4^n}}}


{{{y = (2^2)^n}}}


{{{y = 2^(2n)}}}


{{{log(2,(y)) = 2n}}} Let's call this equation (4)


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Then we would write the following
{{{log(2,(x^2y)) = log(2,(x^2))+log(2,(y))}}} Use equation (1)


{{{log(2,(x^2y)) = 2*log(2,(x))+log(2,(y))}}} Use equation (2)


{{{log(2,(x^2y)) = 2a+log(2,(y))}}} Use equation (3)


{{{log(2,(x^2y)) = 2a+2n}}} Use equation (4)


I don't know where your teacher is getting the 3 in 3a.
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