
Take logarithm on both sides and use the exponent rule of logarithms:
log(a^{b}) = b*log(a)
So applying the rule to the given equation:
3^(x+4)=2^(13x)
log(3^(x+4)) = log(2^(13x))
(x+4)log(3) = (13x)log(2)
Solve the resulting linear equation after substituting numerical values of log(3) and log(2). You can use either natural log (to the base e) or common log (to the base 10).
I get x=1.2 approximately.

i'm sorry i don't understand the last part :(


Evaluate log(3) and log(2) using logarithm to the base 10.
log_{10}3 = 0.4771
log_{10}2 = 0.3010
(x+4)log(3) = (13x)log(2)
0.4771(x+4) = 0.3010(13x)
Solving for x, I get x=1.16 approx.
If you had used logarithm to the base e (natural log), you would have got the same answer of x=1.16 approx.