Discussion

Question:

Solve for integral value x, if ${(5 \sqrt{7})}^{5 x - 4}$ = ${(35)}^{3} {(25)}^{3 / 2}$

Explanation:

Given, ${(5 \sqrt{7})}^{5 x - 4}$ = ${(35)}^{3} {(25)}^{3 / 2}$

⇒ $5^{5 x - 4} \times {(7^{\frac{1}{2}})}^{5 x - 4}$ = $5^{3} \times 7^{3} \times {(5^{2})}^{3 / 2}$

⇒ $5^{5 x - 4} \times 7^{\frac{5 x - 4}{2}}$ = $5^{6} \times 7^{3}$

Since 5 and 7 are prime numbers, power of 5 should be same in LHS and RHS. (Same can be solved w.r.t. power of 7)

⇒ 5x – 4 = 6

⇒ x = 2

Hence, option (a).

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