Question

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

Answer 1

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

Answer 2

NO.

Answer 3

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.