Why $\log a +\ log b$ can be a rational number given $a$ and $b$ are not rational powers of 10?

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I am a high school student who has just started learning about the common logarithms. My teacher said that given a and b are not rational powers of 10, log a + log b can still be a rational number.

I am totally puzzled. Could you guys help me by proving it? But please do not quote some theories that are too advanced for me. Thanks very much!