College Algebra & Trigonometry, 2018a

166 CHAPTER 3. EXPONENTS AND LOGARITHMS
Now, we come back to the question of log b M p =?. This expression (log b M p )is
asking the question ”What power do we raise b to in order to get an answer of
M p ? The result on the previous page shows that:
b px = M p
This means that we must raise b to the px power to get an answer of M p . Remember
that x =log b M. This means that:
b px = M p
so
log b M p = px = p ∗ log b M
This statement of equality is useful if we are trying to solve equations in which
the variable is an exponent.
Example
Solve for x.
4 x =53
We start by taking a logarithm on both of the equation. Just as we can add to both
sides of an equation, or multiply on both sides of an equation, or raise both sides
of an equation to a power, we can also take the logarithm of both sides. So long
as two quantities are equal, then their logarithms will also be equal.
4 x =53
log 4 x = log 53
x log 4 = log 53
x =
log 53
log 4 ≈ 2.864