Question

please solve this question ​

Answer 1

Answer

• The value of x = 1.

Given

• $\underline{\boxed{ \bold{{( {2}^{ - 1} + {4}^{ - 1} + {6}^{ - 1} + {8}^{ - 1} )} ^{x} = 1\cfrac{1}{24}}}}$

To Find

• The value of x.

Step By Step Explanation

Let's solve the equation to find the value of x.

$\longmapsto\sf{{( {2}^{ - 1} + {4}^{ - 1} + {6}^{ - 1} + {8}^{ - 1} )} ^{x} = 1\cfrac{1}{24}} \\ \\ \longmapsto\underline{ \boxed{ \red{ \bold{{a}^{ - 1} = \cfrac{1}{a}} }}} \: \: \: \: \: \bigstar\\ \\\longmapsto\sf{ \bigg( \cfrac{1}{2} + \cfrac{1}{4} + \cfrac{1}{6} + \cfrac{1}{8} \bigg) }^{x} = \cfrac{25}{24} \\ \\\longmapsto\bold{By \: Taking \: LCM} \downarrow \\ \\\longmapsto \sf \bigg( {\cfrac{(1 \times 12) + (1 \times 6) +( 1 \times 4 )+ (1 \times 3)}{24} \bigg)}^{x} = \cfrac{25}{24} \\ \\\longmapsto\sf { \bigg( \cfrac{12 + 6 + 4 + 3}{24} \bigg) = \cfrac{25}{24} }^{x} \\ \\\longmapsto\sf \bigg({\cfrac{25}{24} \bigg)}^{x} = {\bigg( \cfrac{25}{24} \bigg)}^{1} \\ \\ \longmapsto \underline{\boxed{ \bold{ \green{x = 1}}}} \: \: \: \: \: \dag$

Therefore, the value of x = 1.

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Answer 2

Step-by-step explanation:

• this is correct answer
• correct answer