Square root of logarithms

Algebra Level 2

$2^{\sqrt{ \log_2 3 }} - 3^{\sqrt{\log_3 2}} = \, ?$

The answer is 0.

1 solution

Arman Isajanyan
Dec 2, 2017

Note, that $2^\sqrt{log_{2} 3} = (2^{log_{2} 3})^{\frac{1}{\sqrt{log_{2} 3}}} = 3^\sqrt{\frac{1}{\log_{2} 3}} = 3^\sqrt{log_{3} 2}$ . As both members of expression are equal, the answer is 0.

Square root of logarithms

The answer is 0.

1 solution

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