Answered

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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]
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