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Question : 60 of 86

Marks: +1, -0

If

3^{x}=2,5^{y}=3

2^{z}=5

find the value of multiply of

x . y . z

0
1
2
None

Solution:

Concept:

The product

x \cdot y \cdot z

simplifies to

1

by taking logarithms of the given equations.

Explanation:

Given

3^x = 2

, take natural logs:

x \ln 3 = \ln 2 \Rightarrow x = \frac{\ln 2}{\ln 3}

.

Given

5^y = 3

,

y \ln 5 = \ln 3 \Rightarrow y = \frac{\ln 3}{\ln 5}

.

Given

2^z = 5

,

z \ln 2 = \ln 5 \Rightarrow z = \frac{\ln 5}{\ln 2}

.

Multiply:

x \cdot y \cdot z = \frac{\ln 2}{\ln 3} \cdot \frac{\ln 3}{\ln 5} \cdot \frac{\ln 5}{\ln 2} = 1

.

Answer:

1

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