Oblicz x log (podstawa 5) 5 pierwiastek z 125 = x.... Question from @Harss1

October 2018 2 19 Report

Oblicz x log (podstawa 5) 5 pierwiastek z 125 = x

$log_{5}5\sqrt{125}=x\\5^x=5\sqrt{125}\\5^x=5*125^\frac{1}{2}\\5^x=5*(5^3)^\frac{1}{2}\\5^x=5*5^\frac{3}{2}\\5^x=5^\frac{1}{1}*5^\frac{3}{2}\\5^x=5^\frac{2}{2}*5^\frac{3}{2}\\5^x=5^\frac{5}{2}\\x=\frac{5}{2}=2,5$

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vatia

$log_5 5\sqrt{ 125} = x$

$log_5 5\sqrt{25\cdot 5} = x \\log_55\cdot 5\sqrt{5}=x$

$log_525\sqrt{5}=x$

Z definicji logarytmu

$5^x=25\sqrt{5}\\5^x=5^2\cdot 5^{\frac{1}{2}}\\5^x=5^{2\frac{1}{2}}$

$x=2\frac{1}{2}$

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