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?

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.

[tex]\log_2{(0.5)}=-1\ \leftrightarrow\ 2^{-1}=0.5\\\\\log_{0.5}{(2)}=-1\ \leftrightarrow\ 0.5^{-1}=2[/tex]

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?

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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?