Answered

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Can someone solve this question ~
[tex] - 6 \: log_{3}(x - 2) = - 24[/tex]
[tex]ɴᵉᵉᵈ \: ɢᵉⁿᵘⁱⁿᵉ \: ᴀⁿˢʷᵉʳ[/tex]
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Sagot :

DᴀʀᴋPᴀʀᴀᴅᴏx

[tex]\huge \sf༆ Answer ༄[/tex]

The value of x is ~

  • [tex] \sf \: 83[/tex]

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

Let's solve ~

  • [tex] \sf \: - 6 log_{3}(x - 2) = - 24[/tex]

  • [tex] \sf \: log_{3}(x - 2) = \dfrac{ - 24}{ - 6} [/tex]

  • [tex] \sf \: log_{3}(x - 2) = 4[/tex]

  • [tex]x - 2 = {(3)}^{4} [/tex]

  • [tex]x - 2= 81[/tex]

  • [tex]x = 81 + 2[/tex]

  • [tex]x = 83[/tex]

You're welcome spammy ~

abidemiokin

The value of x from the given expression is 5

Laws of logarithm

Given the logarithm expression

  • [tex]-6log_3(x-2)=-24[/tex]

According to the law of logarithm, if [tex]log_ab=c, \ hence \ b= a^c[/tex]

Applying this law to the given question, we can see that:

[tex](x-2)^{-6}=3^{-24}\\(x-2)^6=3^{24}\\(x-2)^6=3^6\\[/tex]

Cancel out the exponents to have:

x - 2  = 3

x = 2 + 3

x = 5

Hence the value of x is 5

Learn more on logarithm here; https://brainly.com/question/25710806

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