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Logarithms

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

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

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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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