Question 3

If $$(\frac{5}{7})^{4x} (\frac{7}{5})^{3x-1} = (\frac{7}{5})^6$$, then the value of x which satisfies the equation.

Solution

Expression : $$(\frac{5}{7})^{4x} (\frac{7}{5})^{3x-1} = (\frac{7}{5})^6$$

=> $$(\frac{7}{5})^{-4x} (\frac{7}{5})^{3x-1} = (\frac{7}{5})^6$$

Using, $$(a)^m\times(a)^n=(a)^{m+n}$$

=> $$(\frac{7}{5})^{-4x+3x-1}=(\frac{7}{5})^6$$

Comparing the exponents, we get :

=> $$-x-1=6$$

=> $$x=-1-6=-7$$

=> Ans - (B)

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