MBApyq

Simplify logarithmic fraction

CAT 2020 Slot 3 · Quantitative Ability · Medium · Logarithms

This is a medium Quantitative Ability question from the CAT 2020 Slot 3 paper. It tests Logarithms. The full answer key and a step-by-step explanation are below — try it yourself first, then reveal the solution.

All CAT 2020 Slot 3 questionsMore Logarithms questionsAll CAT QA

2×4×8×6(log⁡24)2(log⁡48)3(log⁡816)4\frac{2 \times 4 \times 8 \times 6}{(\log_2 4)^2 (\log_4 8)^3 (\log_8 16)^4} equals

Answer

24

Explanation

Numerator = 2×4×8×6=3842 \times 4 \times 8 \times 6 = 384.

Denominator terms: log⁡24=2  ⟹  (log⁡24)2=4\log_2 4 = 2 \implies (\log_2 4)^2 = 4. log⁡48=32  ⟹  (log⁡48)3=278\log_4 8 = \frac{3}{2} \implies (\log_4 8)^3 = \frac{27}{8}. log⁡816=43  ⟹  (log⁡816)4=25681\log_8 16 = \frac{4}{3} \implies (\log_8 16)^4 = \frac{256}{81}.

Denominator = 4×278×25681=4×13×323=1283×33…4 \times \frac{27}{8} \times \frac{256}{81} = 4 \times \frac{1}{3} \times \frac{32}{3} = \frac{128}{3} \times \frac{3}{3} \dots Wait: 4×278×25681=12×27×25681=2566=164 \times \frac{27}{8} \times \frac{256}{81} = \frac{1}{2} \times 27 \times \frac{256}{81} = \frac{256}{6} = 16.

Fraction = 38416=24\frac{384}{16} = 24.

Related Logarithms questions

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