Logarithmic equation for y

CAT 2020 Slot 1 · QA · Medium · Logarithms

If log45=(log4y)(log65)\log_4 5 = (\log_4 y)(\log_6 \sqrt{5}), then yy equals

(TITA)

Answer

36

Explanation

Given: log45=(log4y)(log651/2)\log_4 5 = (\log_4 y)(\log_6 5^{1/2}) log45=(log4y)12log65\log_4 5 = (\log_4 y) \cdot \frac{1}{2} \log_6 5

Divide both sides by log45\log_4 5: 1=log4ylog4512log651 = \frac{\log_4 y}{\log_4 5} \cdot \frac{1}{2} \log_6 5 1=log5y12log561 = \log_5 y \cdot \frac{1}{2 \log_5 6} 2log56=log5y2 \log_5 6 = \log_5 y log562=log5y    y=36\log_5 6^2 = \log_5 y \implies y = 36

Practise this under exam conditions

Sign in to solve it with a live timer, the on-screen CAT calculator, and streak and accuracy tracking across every question you attempt.

Solve in the workspace