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Question
Solve for x: `4^(x-1) × (0.5)^(3 - 2x) = (1/8)^-x`
Solution
`4^(x-1) × (0.5)^(3 - 2x) = (1/8)^-x`
⇒ `(2)^(2^(x - 1)) xx (5/10)^(3 - 2x ) = ( 1/2^3 )^(-x)`
⇒ `(2)^(2x - 2)(2^-1)^(3 - 2x)=(2^-3)^-x`
⇒ `(2)^(2x - 2)(2)^(-3 + 2x)=(2)^(3x)`
⇒ `2^(2x - 2 - 3 + 2x) = (2)^(3x)`
⇒ 2x - 2 - 3 + 2x = 3x
⇒ 4x - 5 = 3x
⇒ 4x - 3x = 5
⇒ x = 5
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