CAT 2020 Question Paper | Quants Slot 3

This question is from Logarithms. Logarithms is one of the most commonly tested topics in the CAT exam. Questions from Exponents and Logarithms have appeared consistently in the CAT exam for the last several years. Questions that appear in CAT tests your basic understanding, like this question, which tests your understanding of the property of logarithms. This topic is easy to master if you practice lots of questions from the CAT Previous Year Question Paper. With every extra hour you log in for this topic, it becomes exponentially simpler.

Question 10 : $\frac{2×4×8×16}{(log_{2}4)^{2}(log_{4}8)^{3}(log_{8}16)^{4}}$ equals

Video Explanation

Explanatory Answer

To start with, we have, $\frac{2×4×8×16}{(log_{2}4)^{2}(log_{4}8)^{3}(log_{8}16)^{4}}$
Let's work on the denominator alone,
log₂⁴ = 2
log₄⁸ = $\frac{log8}{log4}$ = $\frac{log_{2}8}{log_{2}4}$ = $\frac{3}{2}$
log₈¹⁶ = $\frac{log16}{log8}$ = $\frac{log_{2}16}{log_{2}8}$ = $\frac{4}{3}$

So, the denominator becomes, 2 × 2 × $\frac{3}{2}$ × $\frac{3}{2}$ × $\frac{3}{2}$ × $\frac{4}{3}$ × $\frac{4}{3}$ × $\frac{4}{3}$ × $\frac{4}{3}$
= 2 × 4 × 4 × $\frac{4}{3}$
And hence the fraction becomes, $\frac{2×4×8×16}{2 × 4 × 4 × 4/3}$
= $\frac{2 × 4 × 8 × 16 × 3}{2 × 4 × 4 × 4}$
= 2 × 4 × 3 = 24

The question is "$\frac{2×4×8×16}{(log_{2}4)^{2}(log_{4}8)^{3}(log_{8}16)^{4}}$ equals"

Hence, the answer is, ""

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