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Self-marking exercises on evaluating logarithms and using them to solve equations.

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This is level 4 ?  Without a calculator solve the following equations for \(x\). Your answers should be whole numbers or fractions in their lowest terms.

\( \log x = \log 5 + \log 7 \)

\(x=\) Correct Wrong

\( \log24 = \log x + \log 8 \)

\(x=\) Correct Wrong

\( \log 1000 - \log x = \log 50 \)

\(x=\) Correct Wrong

\( \log_2 8 + \log_2 \frac{1}{4} = \log_2 x \)

\(x=\) Correct Wrong

\( \log_7 x = \log_7 (10 - x) \)

\(x=\) Correct Wrong

\( \log_3 x + 2 = \log_3 18 \)

\(x=\) Correct Wrong

\( 2\log x = \log x + 3 \)

\(x=\) Correct Wrong

\( \log_{15} 7 = \log_{15} x + 1 \)

\(x=\) Correct Wrong

\( \log \sqrt{7} = \frac{3}{4} \log 49 - \log x \)

\(x=\) Correct Wrong


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


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Description of Levels



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.

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Level 1 of 6


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

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

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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)