Product of exponents in chain of equations

CAT 2024 Slot 3 · Quantitative Ability · Easy · Algebra

This is an easy Quantitative Ability question from the CAT 2024 Slot 3 paper. It tests Algebra. The full answer key and a step-by-step explanation are below — try it yourself first, then reveal the solution.

All CAT 2024 Slot 3 questions More Algebra questions All CAT QA

If $3^a = 4, 4^b = 5, 5^c = 6, 6^d = 7, 7^e = 8$ and $8^f = 9$ , then the value of the product $abcdef$ is

Answer

Explanation

Using sequential substitution: $4 = 3^a$ $5 = 4^b = (3^a)^b = 3^{ab}$ $6 = 5^c = (3^{ab})^c = 3^{abc}$ $7 = 6^d = 3^{abcd}$ $8 = 7^e = 3^{abcde}$ $9 = 8^f = 3^{abcdef}$

Since $9 = 3^2$ , we have: $3^{abcdef} = 3^2 \implies abcdef = 2$

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

Product of exponents in chain of equations

Explanation

Related Algebra questions

Practise this under exam conditions