Question

Calcule os logaritmos:

log125 625 log243 3 log81 log0,3 0,09 log10  log27/8 

Answer 1

$log_{625}~125 = \\ \\ 625^x = 125 \\ \\ 5^{4x}=5^3 \\ \\ 4x = 3 \\ \\ x = \frac{3}{4}$

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$log_{3}~243 = \\ \\ 3^x = 243 \\ \\ 3^x = 3^5 \\ \\ x = 5$

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$log~81 = 1,90848$

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$log_{0,09}~0,3 = \\ \\ 0,09^x = 0,3 \\ \\ ( \frac{3}{10} )^{2x}= \frac{3}{10} \\ \\ 2x = 1 \\ \\ x = \frac{1}{2}$

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$log10 = \\ \\ 10^x=10 \\ \\ x = 1$

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$log~ \frac{27}{8} = 0,5282$