Review Logarithms

Converting and Evaluating

100

Convert to log form: 3^x = y

log₃ y = x

200

Convert to Exponential Form:

log ₄ x = 5

4⁵ = x

300

Convert to Log Form: 

10^x = 20

log₁₀ 20 = x

400

Evaluate the Log:

log₃ 81= ?

4

500

Evaluate:

log₂ 1/8 = ?

-3

Expand: Properties of Logs

100

Expand the following:

log x²y

2log x + log y

200

Expand the log: log (sqrt(xy))

1/2 log x + 1/2 log y

OR

1/2(log x + log y)

300

Expand using log properties:

log (5x/y²)

log 5 + log x - 2 log y

400

Expand, make sure to evaluate logs if able:

log₂ (8/xy)

log₂ 8 - (log x + log y)     OR    log₂ 8 - log x - log y

OR

3 - (log x + log y)    OR    3 - log x - log y

500

Expand the following, evaluate terms if able:

log₃ 81x²y³z

4 + 2log x + 3log y + log z

Solve Exp Equations

100

Solve for x:

2^3x = 64

x = 2

200

Solve for x: 

4^2x = 32

x = 1.25 or 5/4

300

Solve for x, round your answer to the nearest hundredth:

3^4x = 12

x = 0.57

400

Solve for x, round your answer to the nearest whole number:

2^{x + 4} = 200

x = 4

500

Solve for x, round your answer to the nearest tenth. Make sure to isolate first:

3^{2x + 1} - 5 = 150

x = 1.8

Solve Log Equations

100

log (x + 2) = 2

x = 98

200

log₂(3x - 4) = 5 

x = 12

300

log₃ (2x) - log₃ (5) = 2

x = 22.5

400

log (3x - 5) = log (5x - 15)

x = 5

500

log₄(30 + 17x) - log₄ (2x) = 2

x = 2

Condense: Properties of Logs

100

Condense the logs into a single log:

3 log x + 2 log y - log z

log (x³y²/z)

200

Write as a single log:

5log x + 1/2 log y - 2log z

log(x⁵y^1/2/z²)

You can also have the y as a square root

300

Write as a single log:

2log a - 3log b - 4log c

log (a²/b³c⁴)

400

Write as a single log:

log 2x + log x - log y

log (2x²/y)

500

Write as a single log, then evaluate:

2log₂ 2 + log₂ 6 - log₂ 3

3