[tex]\huge \rm༆ Answer ༄[/tex]
The value of x is ~
[tex] \large \boxed{ \mathfrak{Step\:\: By\:\:Step\:\:Explanation}}[/tex]
Let's solve for x ~
I hope it helped ~
[tex]꧁ \: \large \frak{Eternal \: Being } \: ꧂[/tex]
The value of x in the given equation is [tex]-\frac{4}{5}[/tex]
From the question,
We are to solve the given equation
The given equation is
[tex]log_{6}(36) = 5x +6[/tex]
This becomes
[tex]log_{6}(6^{2} ) = 5x +6[/tex]
From one of the laws of logarithms, we have that
[tex]log_{x}(x^{2} ) = 2log_{x}(x)[/tex]
and
[tex]log_{x}(x) = 1[/tex]
∴ [tex]log_{6}(6^{2} ) = 5x +6[/tex] becomes
[tex]2log_{6}(6) = 5x +6[/tex]
and
[tex]2(1)= 5x +6[/tex]
[tex]2 = 5x +6[/tex]
Now, subtract 6 from both sides
[tex]2-6 = 5x +6-6[/tex]
[tex]-4 = 5x[/tex]
∴ [tex]x = -\frac{4}{5}[/tex]
Hence, the value of x in the given equation is [tex]-\frac{4}{5}[/tex]
Learn more on solving equations here: https://brainly.com/question/11802986
