Pre-Calculus – Solving Exponential Equations using Logs
Name_______________________
Use the Logs Laws to solve the following exponential equations. First, write the exact answer to each
equation (calculator-ready form). Then, write your answer as a decimal to at least four decimal places.
1. 24 x  7
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2. 250  6 x 2
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4. 12(3) x 15(4) x
3. 10  34 x
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6. 900  450(1 .052
)4 x
4
5. 300  50(3) x
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2x 1
 3x1
8. 2
7. 1000  5000(.92)x
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9. 50(1.5)x3  600
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4x
10. 7  8  61
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Solving Exponential Word Problems using Logs
Solve the following problems by first setting up an exponential equation, and then solving it using logs.
1. A high school student with a respiratory infection is given a prescription for antibiotics. His body is able to
metabolize (remove) 17.4% of the drug every hour after it has been taken. The initial dose was 150 mg.
How many hours until the amount of the drug in the student’s body will decrease to below 5 mg?
2. Presently, there are 156 ants in an ant hill. Scientists studying the colony have discovered the ants’
population quadruples every three weeks. Let x  0 correspond with the present population. When will
the population reach 3000?
3. The half-life of Plutonium is 13 years. If 3500 mg are present now, how long will it be until only 800 mg
are left? How long it will take until the ant population reaches 3000?
4. A bank account is started with an initial deposit of $850 and pays 4.22% interest, compounded monthly.
When will the bank account reach $2000?
5. A bank account is started with an initial deposit of $200 and pays 5.46% interest, compounded weekly.
When will the bank account reach $500?