Question

Write 2logx+3log4+log2 as a single logarithm

Answer 1

$log(x ^{2} ) + log(4 {}^{3} ) + log(2) \\ = log( {x}^{2} \times {4}^{3} \times2 )$
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Answer 2

Concept

Logarithm, the exponent or power to which a base must be raised to yield a given number. Expressed mathematically, x is the logarithm of n to the base b if b x = n, in which case one writes x = log b n. logarithm is a function opposite to exponential function)

Given

2logx+3log4+log2

To find

Write in a single logarithm.

Explanation

The expression given as 2logx+3log4+log2.

=log($x^{2}$)+3log($2^{2}$)+log2          

=log($x^{2}$)+6log2)+log(2)         (log m*n=log m+ log n)

=log($x^{2}$)+7log2                      (log m/n)=log m- log n)

=log($x^{2}$+log($2^{7}$)

=log($x^{2}$+128)

Hence 2logx+3log4+log2 can be written as log($x^{2}$+128) which is in single logarithm.

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