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Complete the equation by supplying the missing exponent.

[tex]\[ 3^1 \cdot 3^{-6} = 3^x \][/tex]

A. [tex]\( x = -3 \)[/tex]
B. [tex]\( x = 4 \)[/tex]
C. [tex]\( x = -8 \)[/tex]

Sagot :

GinnyAnswer
Certainly! Let's solve this step-by-step.

We are given the equation:
[tex]\[3^1 \cdot 3^{-6} \cdot 3^x = 3^2\][/tex]

1. We start by combining the exponents of the left-hand side since they have the same base.
[tex]\[3^{1 + (-6) + x} = 3^2\][/tex]

2. Simplify the exponents inside the parentheses:
[tex]\[3^{1 - 6 + x} = 3^2\][/tex]

3. Combine the constants in the exponent:
[tex]\[3^{-5 + x} = 3^2\][/tex]

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

5. Solve for [tex]\(x\)[/tex]:
[tex]\[x = 2 + 5\][/tex]
[tex]\[x = 7\][/tex]

The missing exponent is:
[tex]\[x = 7\][/tex]

Thus, 7 is the value that completes the equation.
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