Express as a single logarithm 3 loga (2x+1) - 2 loga (2x-1) +2

Varela asked May 27, 2023

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Varela asked May 27, 2023

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Answer:

Explanation:

$3 \log_(a) (2x+1)=\log_(a)(2x+1)^(3)$

$2 \log_(a)(2x-1)=\log_(a)(2x-1)^(2)$

$2=\log_(a)(a^(2))$

So the expression can be expressed as a single logarithm as follows:

$3\log_(a)(2x+1)-2\log_(a)(2x-1)+2=\log_(a)(2x+1)^(3)-\log_(a)(2x-1)^(2)+\log_(a)a^(2)$

$3\log_(a)(2x+1)-2\log_(a)(2x-1)+2=\log_(a)\left(((2x+1)^(3)a^(2))/((2x-1)^(2))\right)$

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