Question 977514
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*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \log_b(x^n)\ =\ n\log_b(x)]


Note that *[tex \Large 3125\ =\ 5^5] and that *[tex \Large \sqrt{x}\ =\ x^{\frac{1}{2}}]


So *[tex \LARGE \sqrt{3125}\ =\ \sqrt{5^5}\ =\ 5^{\frac{5}{2}]


So


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \log_5\left(\sqrt{3125}\right)\ =\ \log_5\left(5^{\frac{5}{2}}\right)]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ =\ \frac{5}{2}\log_5(5)]


But *[tex \LARGE \log_b(b)\ =\ 1] so


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ =\ \frac{5}{2}]


John
*[tex \LARGE e^{i\pi}\ +\ 1\ =\ 0]
My calculator said it, I believe it, that settles it

*[tex \Large \ \
*[tex \LARGE \ \ \ \ \ \ \ \ \ \