If 2x = 4y = 8z and xyz = 288, then find

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Target Exam

CUET

Subject

General Test

Chapter

Quantitative Reasoning

Topic

Algebra

Question:

If 2^x = 4^y = 8^z and xyz = 288, then find the value of x.

Options:

Correct Answer:

Explanation:

(2)^x = ((2)²)^y = ((2)³)^z

2^x = 2^2y = 2^3z

So, in this condition, if base is same, then power will be equal

x = 2y = 3z

x = 6R

y = 3R

z = 2R

Now, xyz = 288

6R×3R×2R = 288

36R³ = 288

R³ = 8

R = 2

x =6×2 = 12