Evaluating logarithms worksheet for Precalculus

Precalculus logarithms use fraction bases and fraction answers, and they move freely between log and exponential form. The reliable method is to write the base and the number as powers of the same thing.

Also taught in Algebra 2, at its own level and with its own examples.

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Pick more than one for a sheet that mixes them.

The preview can look cramped on a phone. The PDF and printed sheet come out normal.



Sigma Prep · sigmaprep.io/worksheets Name Evaluating Logarithms Date Period Evaluate or rewrite each logarithm, as asked. Evaluate the logarithm $\log_{9} ⁣ (\frac{1}{9})$ $\log_{1 / 9} (3)$ $\log_{8} (4096)$ $\log_{1 / 8} ⁣ (\frac{1}{2})$ $\log_{12} (1728)$ $\log_{16} ⁣ (\frac{1}{32}) + \ln e^{- 2}$ $\log_{8} ⁣ (\frac{1}{64})$ $\log_{8} (2) + \ln e^{- 2}$ $\log_{7} (16807)$ $\log_{8} (16) + \ln e^{1}$ $\log_{9} (1)$ $\log_{25} ⁣ (\frac{1}{125}) + \ln e^{3}$ $\log_{8} ⁣ (\frac{1}{512})$ Rewrite in logarithmic or exponential form Rewrite in logarithmic form: $3^{1} = 3$ Rewrite in logarithmic form: $4^{- 2} = \frac{1}{16}$ Rewrite in exponential form: $\log_{2} (8) = 3$ Rewrite in exponential form: $\log_{10} ⁣ (\frac{1}{100}) = - 2$ Rewrite in exponential form: $\log_{5} (625) = 4$ Rewrite in logarithmic form: $10^{3} = 1000$ Rewrite in exponential form: $\log_{2} ⁣ (\frac{1}{8}) = - 3$ Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Evaluating Logarithms

Date Period

Evaluate or rewrite each logarithm, as asked.

Evaluate the logarithm
$\log_{9} ⁣ (\frac{1}{9})$
$\log_{1 / 9} (3)$
$\log_{8} (4096)$
$\log_{1 / 8} ⁣ (\frac{1}{2})$
$\log_{12} (1728)$
$\log_{16} ⁣ (\frac{1}{32}) + \ln e^{- 2}$
$\log_{8} ⁣ (\frac{1}{64})$
$\log_{8} (2) + \ln e^{- 2}$
$\log_{7} (16807)$
$\log_{8} (16) + \ln e^{1}$
$\log_{9} (1)$
$\log_{25} ⁣ (\frac{1}{125}) + \ln e^{3}$
$\log_{8} ⁣ (\frac{1}{512})$

Rewrite in logarithmic or exponential form
Rewrite in logarithmic form: $3^{1} = 3$
Rewrite in logarithmic form:
$4^{- 2} = \frac{1}{16}$
Rewrite in exponential form: $\log_{2} (8) = 3$
Rewrite in exponential form:
$\log_{10} ⁣ (\frac{1}{100}) = - 2$
Rewrite in exponential form: $\log_{5} (625) = 4$
Rewrite in logarithmic form: $10^{3} = 1000$
Rewrite in exponential form:
$\log_{2} ⁣ (\frac{1}{8}) = - 3$



Sigma Prep · sigmaprep.io/worksheets Name Evaluating LogarithmsAnswer keyVersion 2 Date Period Evaluate or rewrite each logarithm, as asked. Evaluate the logarithm $\log_{9} ⁣ (\frac{1}{9})$ $- 1$ $\log_{1 / 9} (3)$ $- \frac{1}{2}$ $\log_{8} (4096)$ $4$ $\log_{1 / 8} ⁣ (\frac{1}{2})$ $\frac{1}{3}$ $\log_{12} (1728)$ $3$ $\log_{16} ⁣ (\frac{1}{32}) + \ln e^{- 2}$ $- \frac{13}{4}$ $\log_{8} ⁣ (\frac{1}{64})$ $- 2$ $\log_{8} (2) + \ln e^{- 2}$ $- \frac{5}{3}$ $\log_{7} (16807)$ $5$ $\log_{8} (16) + \ln e^{1}$ $\frac{7}{3}$ $\log_{9} (1)$ $0$ $\log_{25} ⁣ (\frac{1}{125}) + \ln e^{3}$ $\frac{3}{2}$ $\log_{8} ⁣ (\frac{1}{512})$ $- 3$ Rewrite in logarithmic or exponential form Rewrite in logarithmic form: $3^{1} = 3$ $\log_{3} (3) = 1$ Rewrite in logarithmic form: $4^{- 2} = \frac{1}{16}$ $\log_{4} ⁣ (\frac{1}{16}) = - 2$ Rewrite in exponential form: $\log_{2} (8) = 3$ $2^{3} = 8$ Rewrite in exponential form: $\log_{10} ⁣ (\frac{1}{100}) = - 2$ $10^{- 2} = \frac{1}{100}$ Rewrite in exponential form: $\log_{5} (625) = 4$ $5^{4} = 625$ Rewrite in logarithmic form: $10^{3} = 1000$ $\log_{10} (1000) = 3$ Rewrite in exponential form: $\log_{2} ⁣ (\frac{1}{8}) = - 3$ $2^{- 3} = \frac{1}{8}$ Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Evaluating LogarithmsAnswer keyVersion 2

Date Period

Evaluate or rewrite each logarithm, as asked.

Evaluate the logarithm
$\log_{9} ⁣ (\frac{1}{9})$ $- 1$
$\log_{1 / 9} (3)$ $- \frac{1}{2}$
$\log_{8} (4096)$ $4$
$\log_{1 / 8} ⁣ (\frac{1}{2})$ $\frac{1}{3}$
$\log_{12} (1728)$ $3$
$\log_{16} ⁣ (\frac{1}{32}) + \ln e^{- 2}$ $- \frac{13}{4}$
$\log_{8} ⁣ (\frac{1}{64})$ $- 2$
$\log_{8} (2) + \ln e^{- 2}$ $- \frac{5}{3}$
$\log_{7} (16807)$ $5$
$\log_{8} (16) + \ln e^{1}$ $\frac{7}{3}$
$\log_{9} (1)$ $0$
$\log_{25} ⁣ (\frac{1}{125}) + \ln e^{3}$ $\frac{3}{2}$
$\log_{8} ⁣ (\frac{1}{512})$ $- 3$

Rewrite in logarithmic or exponential form
Rewrite in logarithmic form: $3^{1} = 3$ $\log_{3} (3) = 1$
Rewrite in logarithmic form:
$4^{- 2} = \frac{1}{16}$ $\log_{4} ⁣ (\frac{1}{16}) = - 2$
Rewrite in exponential form: $\log_{2} (8) = 3$ $2^{3} = 8$
Rewrite in exponential form:
$\log_{10} ⁣ (\frac{1}{100}) = - 2$ $10^{- 2} = \frac{1}{100}$
Rewrite in exponential form: $\log_{5} (625) = 4$ $5^{4} = 625$
Rewrite in logarithmic form: $10^{3} = 1000$ $\log_{10} (1000) = 3$
Rewrite in exponential form:
$\log_{2} ⁣ (\frac{1}{8}) = - 3$ $2^{- 3} = \frac{1}{8}$

How to do these

$\log_{\frac{1}{4}} 8$

Write both as powers of 2: 1/4 = 2⁻² and 8 = 2³.
(2⁻²)^x = 2³, so -2x = 3.
x = -3/2.

The answer is $- \frac{3}{2}$ .

Where students go wrong

Dropping the negative with a fraction base. A base below 1 raised to a positive power gets smaller, so reaching a number above 1, like 8, needs a negative exponent.

Also called logarithms without a calculator or the meaning of a logarithm.

What you can put on this worksheet

Work out the value: $\log_{3} (81)$ → $4$
Between log and exponential form: Rewrite in logarithmic form: $4^{3} = 64$ → $\log_{4} (64) = 3$
Fraction answers, fraction bases and ln: $\log_{25} (5)$ → $\frac{1}{2}$
Fraction exponents, letters only: Rewrite in logarithmic form:
$64^{\frac{1}{2}} = 8$ → $\log_{64} 8 = \frac{1}{2}$
Letters and numbers mixed: Rewrite in exponential form: $\log_{m} 9 = 3$ → $m^{3} = 9$

Questions about these worksheets

Yes. Every evaluating logarithms sheet is free to print and free to download as a PDF. There is no account to make, no email to hand over and no limit on how many you take.

Yes. The answer key prints on a second page, and you can choose whether it shows each question beside its answer or just the answers in a list.

Yes. Print straight from the page, or download the PDF and print that. The sheet is laid out for paper rather than squeezed off a screen, so there is room to work under each question, and the answer key comes out on its own page.

Precalculus is usually taken around 11th or 12th grade, though schools vary and plenty of students meet it earlier or later. Pick the difficulty rather than the grade: the easy level suits a first lesson on it, the hard level suits review before a test.

Yes, as many as you like. The questions are built fresh each time rather than picked from a fixed set of files, so pressing Generate gives a new sheet. That is what you want for a second class, a retake, or two students sitting next to each other.

That is the closest comparison, and Kuta Software is good software. It is also paid software you install on a computer. These worksheets run in a browser tab for free, with no account and nothing to install. Like Kuta, the evaluating logarithms questions are generated when you ask for them rather than pulled from a fixed set of files, so two classes never get the same sheet, and the answer key comes with it.

Yes. There are two levels, and you can tick more than one for a sheet that mixes them, in which case the questions come out easiest first. The harder levels are not just larger numbers: they ask for something the easy ones do not.

You pick from 5: work out the value, between log and exponential form, fraction answers, fraction bases and ln, fraction exponents, letters only and letters and numbers mixed. Tick as many as you want and set how many of each, or let it spread them evenly.

Reading it as division. log₂ 8 is not 4. Say the sentence out loud every time: two to the what gives eight.

Evaluating logarithms worksheet for Precalculus

Select your difficulty

Evaluate the logarithm

Rewrite in logarithmic or exponential form

Evaluate the logarithm

Rewrite in logarithmic or exponential form

How to do these

Where students go wrong

What you can put on this worksheet

Questions about these worksheets

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