Question

find the value of x , so that (2^-1 +4^-1+6^-1+8^-1)^x =625/576​

Answer 1

SOLUTION

TO DETERMINE

The value of x such that

$\displaystyle \sf{ \bigg( {2}^{ - 1} + {4}^{ - 1} + {6}^{ - 1} + {8}^{ - 1} \bigg) }^{x} = \frac{625}{576}$

EVALUATION

$\displaystyle \sf{ \bigg( {2}^{ - 1} + {4}^{ - 1} + {6}^{ - 1} + {8}^{ - 1} \bigg) }^{x} = \frac{625}{576}$

$\displaystyle \sf{ \implies \: \bigg( \frac{1}{2} + \frac{1}{4} + \frac{1}{6} + \frac{1}{8} \bigg) }^{x} = \frac{625}{576}$

$\displaystyle \sf{ \implies \: \bigg( \frac{12 + 6 + 4 + 3}{24} \bigg) }^{x} = \frac{625}{576}$

$\displaystyle \sf{ \implies \: \bigg( \frac{25}{24} \bigg) }^{x} = \frac{625}{576}$

$\displaystyle \sf{ \implies \: {\bigg( \frac{25}{24} \bigg) }^{x} = {\bigg( \frac{25}{24} \bigg) }^{2} }$

$\displaystyle \sf{ \implies \: x = 2}$

FINAL ANSWER

The required value x = 2

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