The true solution to [tex]3 log 2+log8 =2log(4x)[/tex] is [tex]x=2[/tex]. The correct option is b. [tex]x=2[/tex].
Given expression is
[tex]3 \log 2+\log8 =2\log(4x)[/tex].
We have to calculate the value of [tex]x.[/tex]
Properties of logarithm:
We know that,
[tex]n \log m= \log(m)^n[/tex]
and
[tex]\log m + \log n = \log(mn)[/tex]
Solving the equation:
[tex]3 \log 2+\log8 =2\log(4x)[/tex][tex]\log(2)^3+\log8 =\log(4x)^2[/tex]
{using [tex]n \log m= \log (m)^n[/tex]}
[tex]\log8+\log 8= \log 16x^2[/tex]
[tex]\log (8 \times8)=\log16x^2[/tex] {using [tex]log m + log n = log(mn)[/tex]}
Since log is on both sides so it is eliminated from both sides,
[tex]8 \times8=16x^2\\64=16x^2\\[/tex]
[tex]x^{2} =\frac{64}{16}\\x^{2}=4\\x=2[/tex]
Hence the true solution to [tex]3 log 2+log8 =2log(4x)[/tex] is [tex]x=2[/tex].
For more details on logarithm follow the link:
https://brainly.com/question/163125
