Use properties of logarithms to condense the logarithmic expression log

Globokim8

Globokim8

Answered question

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.

Answer & Explanation

BleabyinfibiaG

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:
log(5)+log(2)
We know that for general logarithm there is base 10.
So rewriting the given logarithmic expression,
log(5)+log(2)=log10{5}+log10{2}
We know properties of logarithm,
log(a)+log(b)log(ab)
=log(ab)1
Applying above property for the given expression, we get
log(a)+log(b)
=log(5)+log(2)log(ab)log(5×2)
=log(10)
Hence, condense expression of logarithm is log(10).
If base of logarithm is 10 then expression value will be
log10{5}+log10{2}=log10{5×2}
log10{10}
=1

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