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An exponential equation is an equation with a variable in the ______________.
Example: _______________
Non-example: _______________
How do you undo an exponent? You use a ___________________. You can think of
logarithms as “base _________________.”
logb(bx) = ____
Special Case for natural logs: ln(ex) = ____
If the logarithm and exponential expression have the same ________, they cancel out. All
that’s left is what’s in the _______________.
Simplify log3(3x + 2) = _________
Example 1: Solve for x.
Simplify ln(e3x – 7) = _________
5x = 32
Step 1: Take the log of both sides.
log5(5x) = ______________
Always use the logarithm with the same __________ as the exponential expression.
For any positive numbers a, b, and c,
with b ≠ 1 and c ≠ 1,
logba =
Step 2: Use the Change of Base formula to rewrite the log.
log5(32) =
 ________
Step 3: Check your answer.
Go back to the original equation and plug in your answer.
52.15  ____
Example 2: Solve for x.
2·3x+5 = 14
_______ = _______
Isolate the exponential term first.
log3(3x+5) = __________
Take the log of both sides. Use the same base.
________ = __________
Simplify. The log cancels the base.
x+5=
Use the Change of Base formula to rewrite the log.
x + 5  _________
Use a calculator to simplify.
x  _______
Solve for x.
Check:
1. Which equation is an exponential equation? _______________
2. Which operation can you use to cancel the base of an exponential expression?
______________________
3. Simplify log4(45x) ______________
5.
4. Simplify ln(ex + 7) ______________
6x + 8 = 2 First step is: ________________________________
6. 5 + 32x = 11 First step is: ______________________________
7.
42x = 13
8. 3 · 5x + 2 = 27
log4(42x) = log4(13)
5x + 2 = 9
______ = ______
log5(5x + 2)= log5(9)
9.
7x = 28
_______ = _______
10. 82x = 24
11.
2 · 5x + 3 = 42
12.
e2x – 6 = 13
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