Quantitative Reasoning

Miscellaneous

Medium

If $243^{3x} = 27^{(4x-1)}$ , then the value of $4^x$ is:

-4

$\frac{1}{4}$

$\frac{1}{16}$

✅ Correct Option: 3

Writing in base 3: $243 = 3^5$ , $27 = 3^3$ . So $3^{15x} = 3^{3(4x - 1)} = 3^{12x - 3}$ . Equating exponents: $15x = 12x - 3 \Rightarrow x = -1$ .

Therefore $4^x = 4^{-1} = \frac{1}{4}$ .

2022: 8 Aug Shift 1

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2026: 31 May Shift 2

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A. 6, 12, 18, 24, ...

B. 0, –2, –4, –6, ...

C. 4, 8, 12, 16, ...

D. 23, 20, 16, ...

Choose the correct answer from the options given below:

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2023: 5 June Shift 2

Find the 50th term of the A.P. 5, 11, 17, 23, ......

If 2433x=27(4x−1)243^{3x} = 27^{(4x-1)}2433x=27(4x−1), then the value of 4x4^x4x is: