CAT 1997 | Question: 109

Question

If $\log_{2}[ \log_{7} (x^{2}-x+37)]=1$ then what could be the value of $x$?

• A. $3$
• B. $5$
• C. $4$
• D. None of these
• E. $c$

Comments

what is the option E?

Answer 1

 

We know that log_a x = y, then x = a^y    

Therefore, on comparing with the given equation we get  log₇ ( x^2 - x + 37 ) = 2^1 = 2 and furthermore from this we can say that x^2 - x + 37 = 7^2 = 49

x^2 - x +37 - 49 = 0

x^2 - x - 12 = 0

on solving the given equation we get x = 4 or x = -3

The value that satisfies the given answer-choices is x = 4.