College Algebra & Trigonometry, 2018a

3.4. SOLVING LOGARITHMIC EQUATIONS 173
Let’s look at an example to see how we’ll use this to solve equations:
Example
Solve for x.
log 2 x +log 2 (x − 4) = 2
The first thing we can do here is to combine the two logarithmic statements into
one. Since log b (M ∗N) =log b M +log b N, then log 2 x+log 2 (x−4) = log 2
[
x(x−4)
]
.
log 2 x +log 2 (x − 4) = 2
log 2
[
x(x − 4)
]
=2
Then we’ll restate the resulting logarithmic relationship as an exponential relationship:
2 2 = x(x − 4)
4=x 2 − 4x
0=x 2 − 4x − 4
4.828, −0.828 ≈ x
Most textbooks reject answers that result in taking the logarithm of a negative
number, such as would be the case for x ≈−0.828. However, the logarithms of
negative numbers result in complex valued answers, rather than an undefined
quantity. For that reason, in this text, we will include all answers.