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Question

Quantitative Aptitude Question on Logarithms

If yy is a negative number such that 2y2log352^{y^2log_35 }= 5log235^{log_23}, then yy equals

A

log2(13)log_2 \bigg(\frac{1}{3}\bigg)

B

log(13)-log \bigg(\frac{1}{3}\bigg)

C

log(15)log \bigg(\frac{1}{5}\bigg)

D

log(15)-log \bigg(\frac{1}{5}\bigg)

Answer

log2(13)log_2 \bigg(\frac{1}{3}\bigg)

Explanation

Solution

The correct option is (A): log2(13)log_2 \bigg(\frac{1}{3}\bigg)

2y2log35=log232^{y^2log_35} = log_23

(2log35)y2=5log23(2log_35)^{y^2} = 5log_23

(5log32)y2=5log23(5log_32)^{y^2} = 5log_23

5y2log32=5log235^{y^2log_32} = 5log_23

y2log32=log23⇒ y^2log_32 = log_23

y2=(log23)(log23)y^2 = (log_23)(log_23)

(is negative)

y=log231y = log_23^{-1} = log213log_2\frac{1}{3}

,