Answered

Get the answers you need at Westonci.ca, where our expert community is always ready to help with accurate information. Explore thousands of questions and answers from a knowledgeable community of experts ready to help you find solutions. Get precise and detailed answers to your questions from a knowledgeable community of experts on our Q&A platform.

Solve [tex]\(3^{x-5}=9\)[/tex]

A. [tex]\(x = -3\)[/tex]
B. [tex]\(x = 2\)[/tex]
C. [tex]\(x = 7\)[/tex]
D. [tex]\(x = 8\)[/tex]

Sagot :

GinnyAnswer
To solve the equation [tex]\( 3^{x-5} = 9 \)[/tex], we can follow these steps:

1. Recognize that 9 can be written as a power of 3. Specifically, [tex]\( 9 = 3^2 \)[/tex].

2. Rewriting the equation [tex]\( 3^{x-5} = 9 \)[/tex] in terms of the same base gives:
[tex]\[ 3^{x-5} = 3^2 \][/tex]

3. Since the bases are the same, we can set the exponents equal to each other:
[tex]\[ x - 5 = 2 \][/tex]

4. Solve for [tex]\( x \)[/tex] by adding 5 to both sides of the equation:
[tex]\[ x - 5 + 5 = 2 + 5 \][/tex]
[tex]\[ x = 7 \][/tex]

The solution to the equation [tex]\( 3^{x-5} = 9 \)[/tex] is [tex]\( x = 7 \)[/tex]. Therefore, the correct answer is:
[tex]\[ x = 7 \][/tex]
Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. We're dedicated to helping you find the answers you need at Westonci.ca. Don't hesitate to return for more.