Practicing Success

Target Exam

CUET

Subject

General Test

Chapter

Quantitative Reasoning

Topic

Algebra

Question:

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

Options:

4

-4

$\frac{1}{4}$

$\frac{1}{16}$

Correct Answer:

$\frac{1}{4}$

Explanation:

$243^{3x}=27^{(4x-1)}$

= $((3)^5)^{3x}=((3)^3)^{(4x-1)}$

15x = 12x - 3

3x = - 3

x = - 1

Now, $4^{x}$ = 4-1

= \(\frac{1}{4}\)