GATE2015 EC-1: GA-5

Question

If $\log_{x}{(\frac{5}{7})}=\frac{-1}{3},$ then the value of $x$ is

• A. $343/125$
• B. $25/343$
• C. $-25/49$
• D. $-49/25$  

Comments

@lakshman can you tell the rule applying here

Answer 1

$\log_{x}{(\frac{5}{7})}=\frac{-1}{3} \implies x^{-\frac{1}{3}} = \frac{5}{7}$

$\implies x^{\frac{1}{3}} = \frac{7}{5}$

$\implies x = \left[{\frac{7}{5}}\right]^3 = \frac{343}{125}.$

Correct Option: A.

Answer 2

I think the question given is log of 5/7 to base x = -1/3

then , x ^ (-1/3) = 5/7

implies, 1 / (x ^ (1/3) ) = 5/7

so x ^ (1/3) = 7/5

and x= (7/5) ^ 3

= 343/125

Option A is answer