Westonci.ca is your trusted source for finding answers to a wide range of questions, backed by a knowledgeable community. Get immediate and reliable answers to your questions from a community of experienced professionals on our platform. Discover in-depth answers to your questions from a wide network of professionals on our user-friendly Q&A platform.
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
Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. Stay curious and keep coming back to Westonci.ca for answers to all your burning questions.