Question

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

Answer 1

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)`