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Solve for x if 3 raised to the power x equals 81.
Ax = 3
Bx = 5
Cx = 4
Dx = 27
Answer & Solution
Correct answer: C. x = 4
1. This is an exponential equation, because the unknown sits in the exponent.
2. The strategy is to express each base in terms of its prime factors.
3. The left hand side already has base 3.
4. Write 81 as a power of 3 by multiplying: 3, 9, 27, 81.
5. That is four factors of 3, so 81 equals 3 raised to the power 4.
6. With the same base on both sides, the exponents can be equated.
7. Therefore x equals 4.
8. Answering 27 confuses a value inside the working with the exponent itself.
_Source: Siyavula Mathematics Grade 11 (Everything Maths, CC BY 4.0), Chapter 1: Exponents and surds_
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