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Question

Solve for x

( 3√4)2x+1/2 = 1/32

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Solution

open parentheses cube root of 4 close parentheses to the power of 2 x plus 1 half end exponent equals open parentheses 4 to the power of 1 third end exponent close parentheses to the power of 2 x plus 1 half end exponent space equals space 4 to the power of fraction numerator 2 x over denominator 3 end fraction plus 1 over 6 end exponent equals 4 to the power of fraction numerator 4 x plus 1 over denominator 6 end fraction end exponent equals open parentheses 2 squared close parentheses to the power of fraction numerator 4 x plus 1 over denominator 6 end fraction end exponent equals 2 to the power of fraction numerator 4 x plus 1 over denominator 3 end fraction end exponent 1 over 32 equals 1 over 2 to the power of 5 equals 2 to the power of negative 5 end exponent i f space b o t h space a r e space e q u a l space comma space fraction numerator 4 x plus 1 over denominator 3 end fraction equals negative 5 s o space x space equals fraction numerator negative 5 cross times 3 space minus 1 over denominator 4 end fraction equals negative 4 space

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