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Solve 2 raised to the power (3x - 1) = 32 for x.
Ax = 5
Bx = 2
Cx = 11
Dx = 3
Answer & Solution
Correct answer: B. x = 2
1. Both sides can be written as powers of the same base, so no logarithm is needed.
2. Rewrite 32 as a power of 2 by counting the doublings: 2, 4, 8, 16, 32.
3. That takes five doublings, so 32 equals 2 to the fifth.
4. The equation now reads 2 to the power 3x minus 1 equals 2 to the fifth.
5. Because the bases match, set the exponents equal: 3x minus 1 equals 5.
6. Adding 1 gives 3x equal to 6, so x equals 2.
7. Answering x = 5 stops at the exponent on the right without solving for x.
8. Answering x = 11 adds 1 and then multiplies by 3 rather than dividing.
9. Answering x = 3 uses 32 as 2 to the fourth, which is 16 rather than 32.
_Source: OpenStax Precalculus (CC BY 4.0), section 4.6 Exponential and Logarithmic Equations_