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Fundamental Laws of Logarithms

The value of ...

Question

The value of $2^{l o g_{3} 5} - 5^{l o g_{3} 2}$ is

A

3

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B

5

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C

2

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Solution

We have
$2^{l o g_{3} 5} - 5 = 2^{l o g_{2} 5 l o g_{3} 2} = (2^{l o g_{2} 5})^{l o g_{3} 2} = (5)^{l o g_{3} 2}$
$∴ 2^{l o g_{3} 5} - 5^{l o g_{3} 2} = 0$

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