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Sagot :
[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 ~
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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