We will rewrite each expression one at a time using the relationship
Notice that the first and third are written as logarithms and the second and fourth are written as exponents. Since a base is not written on the first logarithm, we know it's base 10.
is the exponent. Thus,
The same reasoning applies for the third expression,
Using the same relationship in the opposite way, we can rewrite the second and fourth expression. In 82=64,
it can be seen that 8
is the base and 2
is the exponent. This means that 64
is the value of which we take the logarithm.
For the last expression, this yields
To summarize, the following expressions are equivalent.