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Logarithms

Self-marking exercises on evaluating logarithms and using them to solve equations.
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This is level 1 ?  Use the ^ key to type in a power or index, the underscore _ to type in a subscript and use the forward slash / to type a fraction. Press the right arrow key to end the power, subscript or fraction.

Write an equivalent exponential statement for

\( \log_2 8 = 3\)

Correct Wrong

Write a statement containing a logarithm equivalent to
\(10^2 = 100\)

Correct Wrong

Write an equivalent exponential statement for

\( \log_3 \frac{1}{9} = -2\)

Correct Wrong

Write a statement containing a logarithm equivalent to
\(25^{\frac12} = 5\)

Correct Wrong

Write an equivalent exponential statement for

\( \log_{10} 0.1 = -1\)

Correct Wrong

Write a statement containing a logarithm equivalent to
\(16^{\frac14} = 2 \)

Correct Wrong

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This is Logarithms level 1. You can also try:
Level 2 Level 3 Level 4 Level 5 Level 6

Instructions

Try your best to answer the questions above. Type your answers into the boxes provided leaving no spaces. As you work through the exercise regularly click the "check" button. If you have any wrong answers, do your best to do corrections but if there is anything you don't understand, please ask your teacher for help.

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Description of Levels

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Level 1 - Writing logarithm statements in exponential format and vica versa

Level 2 - Evaluating logarithms without a calculator

Level 3 - Laws of logarithms

Level 4 - Solving equations containing logarithms

Level 5 - Natural logarithms

Level 6 - Solving exponential equations using logarithms

Exam Style Questions - A collection of problems involving logs in the style of GCSE or IB/A-level exam paper questions (worked solutions are available for Transum subscribers).

More Logarithms including lesson Starters, visual aids, investigations and self-marking exercises.

More Exponents including lesson Starters, visual aids, investigations and self-marking exercises.

Answers to this exercise are available lower down this page when you are logged in to your Transum account. If you don’t yet have a Transum subscription one can be very quickly set up if you are a teacher, tutor or parent.

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Logarithms

Level 1 of 6

Tutorial

Find the level you need in the video from these time codes:

Laws of Logarithms

$$ \text{If} \; \log_a b = c \quad \text{then} \; a^c = b$$ $$ \log a + \log b \equiv \log ab$$ $$ \log a - \log b \equiv \log \frac{a}{b}$$ $$a \log b \equiv \log b^a $$

Changing Base

$$ \log_a b = \frac{ \log_c b}{ \log_c a}$$

Don't wait until you have finished the exercise before you click on the 'Check' button. Click it often as you work through the questions to see if you are answering them correctly. You can double-click the 'Check' button to make it float at the bottom of your screen.

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Typing Mathematical Notation

These exercises use MathQuill, a web formula editor designed to make typing Maths easy and beautiful. Watch the animation below to see how common mathematical notation can be created using your keyboard.

MathQuill Animation

Use ^ for index/exponent

Use _ for the base of a logarithm

Use space and tab to get down from the index position or up from the subscript position

No brackets required for the log function - write log10 rather than log(10)

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