Question

4.Write the laws of logarithms​

Answer 1

Answer:

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Step-by-step explanation:

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Answer 2

Answer:

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Step-by-step explanation:

The laws of logarithms

mc-bus-loglaws-2009-1

Introduction

There are a number of rules known as the laws of logarithms. These allow expressions involving

logarithms to be rewritten in a variety of different ways. The laws apply to logarithms of any base

but the same base must be used throughout a calculation.

The laws of logarithms

The three main laws are stated here:

First Law

log A + log B = log AB

This law tells us how to add two logarithms together. Adding log A and log B results in the logarithm

of the product of A and B, that is log AB.

For example, we can write

log10 5 + log10 4 = log10(5 × 4) = log10 20

The same base, in this case 10, is used throughout the calculation. You should verify this by

evaluating both sides separately on your calculator.

Second Law

log A − log B = log A

B

So, subtracting log B from log A results in log A

B

.

For example, we can write

loge 12 − loge 2 = loge

12

2

= loge 6

The same base, in this case e, is used throughout the calculation. You should verify this by evaluating

both sides separately on your calculator.

Third Law

log A

n = n log A

So, for example

log10 5

3 = 3 log10 5

You should verify this by evaluating both sides separately on your calculator. our

Two other important results are

www.mathcentre.ac.uk 1 c mathcentre 2009