Answered

Westonci.ca is your go-to source for answers, with a community ready to provide accurate and timely information. Experience the ease of finding quick and accurate answers to your questions from professionals on our platform. Explore comprehensive solutions to your questions from knowledgeable professionals across various fields on our platform.

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

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

We appreciate your time. Please come back anytime for the latest information and answers to your questions. We hope this was helpful. Please come back whenever you need more information or answers to your queries. Thank you for using Westonci.ca. Come back for more in-depth answers to all your queries.