How to resolve the logarithm?

Question

I have this exercise:

My result is : $16/3$, but it does not appear in the answers, what is wrong?

Or is it another representation of the same logarithm?

Answer 1

Let apply the usual rules for logarithm

$$\log_a b=\frac{1}{\log_b a} \quad \quad \log_a b^c=c\cdot \log_a b$$

thus

$$\log_{27}3+\log_2 32=\frac{1}{\log_3 3^3}+\log_2 2^5=\frac13+5=\frac{16}3$$

Answer 2

I think you are right: $$\log_{27}3+\log_232=\frac{1}{3}+5.$$