Why does $\log_{4}32 \neq \log _{4}(4 \cdot 8)$

Question

$$\log_{4}32=2.5$$

If $$\log_{a}(b\cdot c) = \log _{a}b + \log_{a}c \,\,\,; (a>0, b>0,c>0, a\neq 1)$$

Then why does $\log_{4}32$ can't be $\log _{4}(4 \cdot 8)= \log_{4}4+\log_{4}8 = 1+2=3$?

Answer 1

Because $\log_4(8) \neq 2$. Instead, $4^2=16$.