College Algebra & Trigonometry, 2018a

3.3. SOLVING EXPONENTIAL EQUATIONS 167
Since the log base 10 and log base e are both programmed into most calculators,
these are the most commonly used bases for logarithms.
Example
Solve for x.
5 2x+3 =17
We start this problem in the same fashion, but this time we will use a logarithm
to the base e:
5 2x+3 =17
ln 5 2x+3 =ln17
(2x +3)ln5=ln17
There are several possibilities for finishing the problem from this point. We will
focus on two of them that are the most useful for solving more complex problems.
First, we will distribute the ln 5 into the parentheses and then get the x by itself.
(2x +3)ln5=ln17
x ∗ 2 ln 5 + 3 ln 5 = ln 17
−3ln5=−3ln5
x ∗ 2ln5=ln17− 3ln5
x =
ln 17 − 3ln5
2ln5
≈−0.620
And we can check the answer by plugging it back in:
5 2∗(−0.0620)+3 ≈ 5 1.760 ≈ 16.9897 ≈ 17