Answered

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How do you solve for x?
[tex] log_{6}(36) = 5x + 6[/tex]
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Sagot :

DᴀʀᴋPᴀʀᴀᴅᴏx

[tex]\huge \rm༆ Answer ༄[/tex]

The value of x is ~

  • [tex] -0.8 [/tex]

[tex] \large \boxed{ \mathfrak{Step\:\: By\:\:Step\:\:Explanation}}[/tex]

Let's solve for x ~

  • [tex] \sf \: log_{6}(36) = 5x + 6[/tex]

  • [tex] 2 = 5x + 6[/tex]

  • [tex]5x = 2 - 6[/tex]

  • [tex]x = - 4 \div 5[/tex]

  • [tex]x = - 0.8[/tex]

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

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