Use properties of logarithms to find the exact value of the expression. log5 625- log4(1/16)

Question

kinggeorge · Answer

Can you solve $\log_5(625)$ and $\log_4(1/16)$?

anonymous · Answer

NO.

kinggeorge · Answer

Let's start with $\log_5(625)$ then. By the properties of logarithms, $$\log_5(625)=x \Longrightarrow 5^x=625$$Using a little guess and check, it's easy to see that $x=4$. Thus $\log_5(625)=4$.

If we move on to $\log_4(1/16)$, we know that$$\log_4\left({1\over16}\right)=y \Longrightarrow 4^y=\left({1\over16}\right)$$So once again using a little guess and check, we find $y=-2$. Thus $\log_4(1/16)=-2$.You should be able to solve it from here.