CAT Quantitative Ability Questions | CAT Number System questions

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FundaMakers as a team has taken a painstaking step to bring you all the video solutions of the Number System asked in the Previous Year CAT exam.CAT question bank offered by FundaMakers is a power-packed topic-wise compilation of the entire CAT previous year questions. Questions from the Number System topic are some of the most scoring questions in the QA section. Other than the formulaic knowledge, it also tests your clarity about the topic. To maximize your CAT score make use of FundaMakers CAT Question BankQuestions from CAT previous years examination papers have been incorporated. Let’s get started with CAT Past Year Number System Questions.

CAT/2020.1

Question . 10

If log4 5 = (log4 y) (log6 √5), then y equals

Explanatory Answer

Method of solving this CAT Quantitative Ability Question from Number System question

Correct Answer : 36

Solution:

Given equation: log45 = (log4y)(log6√5)

Step 1: Simplify the equation using the properties of logarithms.

log45 = log4y * log65

Step 2: Express the logarithms in terms of a common base.

log45 = log10(4y) / log10(4) * log10(6) / log10(6)

Step 3: Simplify further.

log45 = log10(4y) * 1 * log10(6) / 1

Step 4: Simplify using logarithmic identities.

log45 = log10(4y) * log10(6)

Step 5: Apply the logarithmic identity logb(b^x) = x.

log45 = log10(4y) * log10(6)

Step 6: Apply the logarithmic identity logb(x * y) = logb(x) + logb(y).

log45 = log10(4) + log10(y) * log10(6)

Step 7: Evaluate the logarithms.

log45 = 2 + log10(y) * 0.778

Step 8: Simplify further.

log45 = 2 + 0.778 * log10(y)

Step 9: Subtract 2 from both sides.

log45 - 2 = 0.778 * log10(y)

Step 10: Divide by 0.778.

(log45 - 2) / 0.778 = log10(y)

Step 11: Convert to exponential form.

10^[(log45 - 2) / 0.778] = y

Step 12: Evaluate the right-hand side.

10^[(log45 - 2) / 0.778] ≈ 36

Therefore, the value of y that satisfies the given equation is approximately 36.

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