Globokim8

2021-08-11

Use properties of logarithms to condense the logarithmic expression log 5 + log 2. Write the expression as a single logarithm whose coefficient is 1. Where possible, evaluate logarithmic expressions without using a calculator.

BleabyinfibiaG

Skilled2021-08-12Added 118 answers

We have to condense the logarithmic expression as well as we have to find the exact value where expression is:

$\mathrm{log}\left(5\right)+\mathrm{log}\left(2\right)$

We know that for general logarithm there is base 10.

So rewriting the given logarithmic expression,

$\mathrm{log}\left(5\right)+\mathrm{log}\left(2\right)={\mathrm{log}}_{10}\left\{5\right\}+{\mathrm{log}}_{10}\left\{2\right\}$

We know properties of logarithm,

$\mathrm{log}\left(a\right)+\mathrm{log}\left(b\right)\mathrm{log}\left(ab\right)$

$=\mathrm{log}\left(ab\right)1$

Applying above property for the given expression, we get

$\mathrm{log}\left(a\right)+\mathrm{log}\left(b\right)$

$=\mathrm{log}\left(5\right)+\mathrm{log}\left(2\right)\mathrm{log}\left(ab\right)\mathrm{log}(5\times 2)$

$=\mathrm{log}\left(10\right)$

Hence, condense expression of logarithm is$\mathrm{log}\left(10\right)$ .

If base of logarithm is 10 then expression value will be

$\mathrm{log}}_{10}\left\{5\right\}+{\mathrm{log}}_{10}\left\{2\right\}={\mathrm{log}}_{10}\{5\times 2\$

$\mathrm{log}}_{10}\left\{10\right\$

=1

We know that for general logarithm there is base 10.

So rewriting the given logarithmic expression,

We know properties of logarithm,

Applying above property for the given expression, we get

Hence, condense expression of logarithm is

If base of logarithm is 10 then expression value will be

=1

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