Exponential and Logarithmic Functions

Conversions

100

Convert this log statement to exponential form: Log₂ 32 = 5

What is 2⁵ = 32?

200

Convert this to logarithmic form: 4⁵=1024.

What is log₄ 1024 = 5?

300

Convert to exponential form: log₃ 81 = 4.

What is 3⁴ = 81?

400

Convert e³ = 20.09 to a logarithm statement.

What is ln 20.09 = 3?

500

Convert ln 6 = x to an exponential equation.

What is e^x = 6?

Change of Base

100

Find log₃20 = x

What is 2.7268?

200

Find log₄ 9.

What is 1.585?

300

Find log₈ 8⁵.

What is 5?

400

Find log₃ 8.

What is 1.893?

500

Find ln 10.

What is 2.303?

Solutions to Exp Equations

100

Find 4^x=64.

What is 3?

200

Find 3^x = 21.

What is 2.771?

300

Find 7 = 2^3x.

What is 0.936?

400

Solve:  64^y = 16^{y + 2}.

What y = 2.

500

Solve:  3e^x + 2 = 23.

What is 1.9459?

Log Equations

100

Solve:  log (4x-3) = log 19.

What is 11/2?

200

Solve:  log₆ (x - 4) = log₆ 25

What is 29?

300

Solve:  log x + log (x + 4) = log 12.

What is 2?

400

Solve:  log 5 - log (2x - 1) = 1.

What is 3/4?

500

Solve:  log₅ x + log₅ (x + 24) = 2.

What is 1?

Logs rule!

100

Expand the following Logarithm using the Product Rule

log_2 xy

log_2 x+log_2 y

200

Compress the following logarithm using the quotient rule.

log10-logx

log(10/x)

300

Rewrite the following logarithm using the power rule.

log5^2

2 log 5

400

Expand the following logarithm using the power and quotient rules.

log(5/x^2)

log 5 -2log x

500

Compress the following logarithm using the power and product rules.

1/2 logx+3log 4

log(x^(1/2)4^3)