Mathematics
Grade10
Easy

Question

Solve  2 equals open parentheses 4 to the power of 1 third end exponent close parentheses open parentheses 2 to the power of x over s end exponent close parentheses

  1. 2
  2. 5
  3. 1
  4. 9

hintHint:

1 right parenthesis space a to the power of m cross times a to the power of n equals a to the power of m plus n end exponent
2 right parenthesis space space a to the power of m equals a to the power of n
space space space space space space space m equals n

The correct answer is: 1


    2 equals open parentheses 4 to the power of 1 third end exponent close parentheses open parentheses 2 to the power of x over 3 end exponent close parentheses
    2 to the power of 1 equals open parentheses 2 to the power of 2 over 3 end exponent close parentheses open parentheses 2 to the power of x over s end exponent close parentheses
    2 to the power of 1 equals left parenthesis 2 right parenthesis to the power of 2 over 3 plus x over 3 end exponent
    2 to the power of 1 equals left parenthesis 2 right parenthesis to the power of fraction numerator n plus 2 over denominator 3 end fraction end exponent
    fraction numerator x plus 2 over denominator 3 end fraction equals 1   [Since the bases are equal, equate the powers]
    x plus 2 equals 3
    x equals 1

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