# Logarithms

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

##### Level 1Level 2Level 3Level 4Level 5Level 6Exam-StyleDescriptionHelpMore on Exponents

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$$16^{\frac14} = 2$$ =
Check

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.

When you have got all of the questions correct you may want to print out this page and paste it into your exercise book. If you keep your work in an ePortfolio you could take a screen shot of your answers and paste that into your Maths file.

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## Go Maths

Learning and understanding Mathematics, at every level, requires learner engagement. Mathematics is not a spectator sport. Sometimes traditional teaching fails to actively involve students. One way to address the problem is through the use of interactive activities and this web site provides many of those. The Go Maths page is an alphabetical list of free activities designed for students in Secondary/High school.

## Maths Map

Are you looking for something specific? An exercise to supplement the topic you are studying at school at the moment perhaps. Navigate using our Maths Map to find exercises, puzzles and Maths lesson starters grouped by topic.

## Teachers

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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 in the style of GCSE or IB/A-level exam paper questions (worked solutions are available for Transum subscribers).

More on 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.

## Logarithms

$$\text{If} \; \log_a b = c \quad \text{then} \; a^c = b$$

## Tutorial

The video above is from Khan Academy

## Laws of Logarithms

$$\log a + \log b \equiv \log ab$$ $$\log a - \log b \equiv \log \frac{a}{b}$$ $$a \log b \equiv \log b^a$$

## 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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