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To evaluate the common logarithm of a number can be seen as finding what exponent the number $10$ must be raised to in order to get that number. Here, we take the logarithm of the number $10_{78}.$ We already know that we raise $10$ to $78$ to get that number. Therefore, we can evaluate the logarithm immediately. $g(10_{78})=78$ We can just read what the exponent is in the argument of the function. This is always true when evaluating the common logarithm of a power with the base $10.$

$g(10_{78})$

$g(10_{m})=m$

$78$

b

The same reasoning applies here. The number $10_{-36}$ is accuired by raising $10$ to $-36.$

$g(10_{-36})$

$g(10_{m})=m$

$-36$

c

Here we need to rewrite the number as a power of ten. The logarithm will then be determined as in the previous calculations.

$g(10001 )$

WritePowWrite as a power

$g(10_{3}1 )$

FracToNegExponent$a_{m}1 =a_{-m}$

$g(10_{-3})$

$g(10_{m})=m$

$-3$