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If \( \Large 3^{x}=5^{y}=45^{z} \), then
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A) \( \Large x+y+z=0 \) |
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B) \( \Large \frac{2}{x}=\frac{1}{z}-\frac{1}{y} \) |
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C) \( \Large \frac{2}{y}=\frac{1}{x}-\frac{1}{z} \) |
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D) \( \Large \frac{2}{z}=\frac{1}{y}-\frac{1}{x} \) |
Correct Answer:
| B) \( \Large \frac{2}{x}=\frac{1}{z}-\frac{1}{y} \) |
Description for Correct answer:
Let \( \Large 3^{x} = 5^{y} = 45^{z} = k \)
=> \( \Large 3=k^{\frac{1}{x}},\ 5=k^{\frac{1}{y}},\ and\ 45=k^{\frac{1}{z}} \)
Now \( \Large \left(3^{2} \times 5\right) = k^{\frac{1}{z}} \)
=> \( \Large \left(k^{\frac{1}{x}}\right)^{2} \times k^{\frac{1}{y}} = k^{\frac{1}{z}} \)
=> \( \Large \frac{2}{x}+\frac{1}{y}=\frac{1}{z} \)
\( \Large \therefore \frac{2}{x}=\frac{1}{z}-\frac{1}{y} \)
Part of solved Polynomials questions and answers : >> Elementary Mathematics >> Polynomials
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