Solve log base 3 of (x − 1) = 2.

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Multiple Choice

Solve log base 3 of (x − 1) = 2.

Explanation:
When you see log base 3 of (x−1) = 2, use the inverse relation between logs and exponents: if log base b of A equals C, then A equals b^C. Here A is x−1, b is 3, and C is 2, so x−1 = 3^2 = 9. Thus x = 10. The logarithm also requires its input to be positive, so x must be greater than 1; 10 satisfies that. Quick check: log base 3 of (10−1) is log base 3 of 9, which is 2, so it works.

When you see log base 3 of (x−1) = 2, use the inverse relation between logs and exponents: if log base b of A equals C, then A equals b^C. Here A is x−1, b is 3, and C is 2, so x−1 = 3^2 = 9. Thus x = 10. The logarithm also requires its input to be positive, so x must be greater than 1; 10 satisfies that. Quick check: log base 3 of (10−1) is log base 3 of 9, which is 2, so it works.

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