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Algebra Level 2

A real x x satisfy the equation 1 6 x = 64 16^x = 64 . What is the value of 16 x 16x ?


The answer is 24.

Pi Han Goh by Pi Han Goh , 30, Malaysia

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2 solutions

Viki Zeta
Nov 12, 2016

1 6 x = 64 4 2 x = 4 3 2 x = 3 16 x = 24 16^x = 64 \\ 4^{2x} = 4^3 \\ 2x = 3 \\ 16x = 24

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Can you explain in detail.

Kanta Sharma - 4 years, 7 months ago

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which step?

Viki Zeta - 4 years, 7 months ago
Munem Shahriar
Nov 27, 2017

1 6 x = 64 16^x = 64

⇒ ( 4 2 ) x = 4 3 \Rightarrow (4^2)^x = 4^3

⇒ 4 2 x = 4 3 \Rightarrow 4^{2x} = 4^3

⇒ 2 x = 3 \Rightarrow 2x = 3

⇒ x = 3 2 \Rightarrow x = \dfrac32

Hence 16 x = 16 ( 3 2 ) = 24 16x = 16 \left(\frac32\right ) = \boxed{24}

1 Helpful 0 Interesting 0 Brilliant 0 Confused

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