Find the sum, difference, or product of logarithms as a

sjeikdom0

sjeikdom0

Answered question

2021-08-10

Find the sum, difference, or product of logarithms as a single logarithm, if it is possible, using the properties of logarithms
log413log4a

Answer & Explanation

aprovard

aprovard

Skilled2021-08-11Added 94 answers

The logarithm is
log413log4a
The objective is to use the property of logarithm to combine the terms in single logarithm
The product rule of the logarithm is: for any base a>0, a ne 1
loga(uv)=logau+logav
The power rule of logarithm is: a>0, a ne 1, and any exponent value n,
loga(un)=nlogau
The quotient rule of the logarithm is for any base a>0, a ne 1
loga(uv)=logaulogav
To combine the logarithmic expression into single logarithm, the bases of logarithm must be same
So, the given logarithmic expression is converted into single logarithm using properties of logarithm
log413log4a=log413a
The answer is log413a

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