Question

I just did a change of base and divided the logs. The answer was negative. I thought logs couldn't give negative answers?

Am I confusing the rule?

Is the rule only applied to the logs and not the solution?

Answer 1

a logarithm can have any value

Explanation:

The range of logarithms to any positive base (excluding 1) is "all real numbers", which includes negative numbers. A logarithm is an exponent (of the base). An exponent can have any value.

Here are a couple of examples of logarithms that have a negative value.

`\log_2{(0.5)}=-1\ \leftrightarrow\ 2^(-1)=0.5\\\\log_0.5((2))=-1\ \leftrightarrow\ 0.5^(-1)=2`