Exponents and Logarithms

Rewrite

100

Write as a log: 3⁵=243

What is log₃(243)=5?

200

Write in exponential form: log₅125=3

What is 5³=125?

300

Rewrite as exponential: log₄2

what is 4^x=2?

400

Rewrite log₆x=45 as exponential

What is 6⁴⁵=x

500

Rewrite as a log: x⁵=1024

What is log_x1024=5

Solve (no calculator)

100

Solve 2^x = 128

What is x = 7?

200

Solve log x = -3.

what is x = 1/1000?

300

Evaluate: log₈₁3

what is x = 1/4

400

What is the change of base formula if log₅10 = x?

log(10)/log(5)

500

Solve e^(2x + 7) = e^(3x -1)

what is x = 8?

Expand

100

Expand log(5x)

What is log 5 + log x?

200

Expand ln(x² y⁵).

What is 2lnx + 5lny

300

Expand log(3xyz/4)

What is log 3 + log x + log y + log z - log 4?

400

Expand ln(3x²z³/5x).

What is ln 3 + 2lnx + 3lnz - (ln 5 + ln x)?

500

Expand log(x²/y⁵z⁴)^1/2

What is 1/2(2log x - 5log y - 4log z) OR logx - 5/2logy - 2logz?

Condense

100

Condense log 7 + log b

What is log 7b?

200

Condense 4log 2 + 3log 4

What is log 1024?

300

Condense ln x + ln 3 + 2ln y -ln e

What is ln(3xy²)-1?

400

Condense 1/3logx - 2/3log y

What is log x^1/3/y^2/3?

500

Condense 1/2(3log x + 3log y - 7log z).

What is log(x³y³/z⁷)^1/2

Solve (yes calculator)

100

Solve log₈1?

What is x = 0?

200

log₂(3x-6) = log₂(2x+7)

What is x = 13?

300

Solve e^(2x + 7) = e^(3x - 1)

What is 8?

400

2e^x+1-3 = 33

What is x = 1.890?

500

Solve 8^x+2+2=3

What is x = -2?