Exponential & Log Equations

Exponential Equations

100

Solve

2^{5x + 1} = 32

What is 4/5 (or 0.8)?

200

Solve.  Round your answer to 3 decimals if needed.

5 - 3^x = -40

What is 3.465?

300

Solve.  Round your answer to 3 decimals if needed.

9^{2x - 5} = 729^{x + 3}

What is -14?

400

Solve, giving the exact value for x.

5(2)^{4 - x} = 200

What is 4 - log₂40?

500

Solve, giving the exact value for x.

7 - 2e^x/2 = 1

What is 2 ln3 (or ln 9)?

Log Equations

100

Solve.  Round your answer to 3 decimals if needed.

ln 3x = 6

What is 134.476?

200

Solve, giving the exact value for x.

log (4x - 3) = 2

What is 103/4 (or 25.75)?

300

Solve, giving the exact value for x.

log 5x - 3 = 2

What is 20000??

400

Solve, giving the exact value for x.

log (6x + 35) = log (8x - 5)

What is 20?

500

Solve, give the exact value(s).

ln 2x² = 2

What is + square root (0.5e²)?  

Properties

100

Condense into one logarithm

log 40 - log 4 + log 2

What is log 20?

200

Condense into one logarithm

log 800 - log 25 - 2 log 4

What is log 2?

300

Condense into one logarithm

2 ln 8 - 3 ln 4

What is ln 1?

400

Solve.  Round your answer to 2 decimals if needed.

ln x + ln 3x = 14

What is 633.14?

500

Solve.  Round your answer to 3 decimals if needed.

log (7x + 1) = log (x - 2) + 1

What is 7?

Applications

100

A research has found that a new antibiotic causes a bacteria to decline rate of 16% an hour.  How long will it take for 8000 bacteria to shrink to 500 bacteria?Round your answer to the nearest tenth of an hour.

What is 15.9 hours?

200

Mandy invests $3500 in an account that pays 6.7% interest compounded continuously.  How long will it take for her to have at least $12,000?  Round your answer to the nearest tenth of a year.

What is 18.4 years?

300

The battery power available to run a satellite is given by the formula P = 50e^-0.004t, where P is the power in watts and t is the time in days.  For how many days can the satellite run with (a minimum of) 15 watts of power?

What is 300 days?

400

A fossil contains 35% of its original carbon-14.  The half-life of carbon-14 is 5730 years.  What is the age of the fossil?  Round to the nearest tenth of a year.

What is 8678.5 years?

500

A culture of 10 bacteria is started, and the number of bacteria double every 2 hours.  In about how many hours will there be 3 million bacteria?  Round your answer to the nearest tenth of an hour.

What is 36.4 hours?

Surprise Me

100

The inverse of an exponential function.

What is a logarithm?

200

The base and the argument of logarithms are these types of numbers.

What are positive numbers.

300

The solution to 

log 5 - log 2x = 1

What is 1/4?

400

The product of the solutions to 

log₇(2x - 3)² = 2

What is -10?

(x = 5, -2)

500

The solution to 

log 9 - log x + 1 = 6

What is 9 x 10^-5?