Using Properties of Logarithms

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. $$\log \left(10^{78}\right)=78$$ 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 $10.$

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

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