Question

log base(16) 32 = x + 2.

Answer 1

\[\LARGE \log_{16}(32)=x+2\]
\[\LARGE \log_{2^4}(2^5)=x+2\]
\[\LARGE \frac14 \cdot 5 \cdot \log_{2}(2)=x+2\]
\[\LARGE \frac54 \cdot 1=x+2\]
can you do it now ? :)

Answer 2

raise both sides to powers of 16

32 = 16^(x+2)

32 = 16^(5/4)

then

16^(5/4) = 16^(x + 2)

equate the powers

5/4 = x + 2

x = -3/4