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The common logarithm of a number is the exponent you have to raise $10$ by, to get the desired number. For example,

$\lg(100)=2 \quad \text{because} \quad 10^2=100.$

In the similarity $10^2=100$, you could just as easily replace the exponent with $\lg(100)$ since this is equal to $2.$ If a logarithm, $\lg\left(a\right),$ is an exponent to $10$, you can directly determine the power of ten value by reading of the logarithms argument, $a.$

Overall, this can be written in the following way.

$10^{\lg(a)}=a$

You can only calculate logarithms of positive numbers. There's no number that you can raise 10 to in order to get zero or a negative result. As a result, this identity applies only when $a > 0.$