IDNLearn.com: Where your questions meet expert answers and community support. Explore thousands of verified answers from experts and find the solutions you need, no matter the topic.
Sagot :
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]
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 joining our conversation. Don't hesitate to return anytime to find answers to your questions. Let's continue sharing knowledge and experiences! IDNLearn.com provides the best answers to your questions. Thank you for visiting, and come back soon for more helpful information.