If (1/7) ^ 4-2x = root 7 Find the value of x Please tell me how to solve - Maths - Number Systems

Question

If (1/7) ^ 4-2x = root 7 Find the value of x Please tell me how
to solve this problem

Pooja · Accepted Answer

${(\frac{1}{7})}^{4 - 2 x} = \sqrt{7} = 7^{\frac{1}{2}} \Rightarrow {(7^{- 1})}^{4 - 2 x} = 7^{\frac{1}{2}} \Rightarrow {(7)}^{2 x - 4} = 7^{\frac{1}{2}}$

Now, when base is same, powers or exponents can be equated, thus we get

$2 x - 4 = \frac{1}{2} \Rightarrow 2 x = 4 + \frac{1}{2} = \frac{9}{2} \Rightarrow x = \frac{9}{2} \times \frac{1}{2} = \frac{9}{4} (A n s w e r)$

If (1/7) ^ 4-2x = root 7. Find the value of x. Please tell me how to solve this problem.