# 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$$\log_2 8 = 3$$ Write a statement containing a logarithm equivalent to$$10^2 = 100$$ Write an equivalent exponential statement for$$\log_3 \frac{1}{9} = -2$$ Write a statement containing a logarithm equivalent to$$25^{\frac12} = 5$$ Write an equivalent exponential statement for$$\log_{10} 0.1 = -1$$ Write a statement containing a logarithm equivalent to$$16^{\frac14} = 2$$
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This is Logarithms level 1. You can also try:
Level 2 Level 3 Level 4 Level 5 Level 6

## Instructions

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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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Level 1 of 6

## Tutorial

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

• 1:06 :: Level 1 - Writing log statements in index format and vica versa
• 4:30 :: Level 2 - Evaluating logarithms without a calculator
• 7:00 :: Level 3 - Laws of logarithms
• 10:45 :: Level 4 - Solving equations containing logarithms
• 12:25 :: Level 5 - Natural logarithms
• 13:14 :: Level 6 - Solving exponential equations using logarithms

## 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.

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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