alleryStart learning →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_
Keep practising Exponents and surds
Browse all Exponents and surds questions for ZIMSEC O-Level, or explore more Mathematics topics.
Related questions
Catch every real number typeRationalising the denominator of 6 divided by the square root of 3 gives which expression?Which strategy is used first when an exponential expression is manipulated?Written in simplest surd form, the square root of 50 becomes which expression?What happens to a fraction when its denominator is rationalised?An even root is being taken. What must be true of the radicand for the root to be real?Which name is also used for an exponent?What is a radical called when it works out to an irrational number?