LOGARYTM

${\log }_{a}b=c\text{, gdy }{a}^c=b$

$a>0,a\ne 1,b>0,c\in \mathbb{R}$

WZORY

${\log }_{a}b+{\log }_{a}c={\log }_a\left(a\cdot b\right)$

${\log }_{a}b-{\log }_{a}c={\log }_a\left(a:b\right)$

$a^{{\log }_{a}b}=b$

$n\cdot {\log }_{a}b={\log }_a{b}^n$

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a)

$3^{{\log }_{3}5}=5$

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b)

${\left(\frac{1}{2}\right)}^{{\log }_{\frac{1}{2}}6}=6$

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c)

$2^{-{\log }_{\frac{1}{2}}3}={\left(\frac{1}{2}\right)}^{{\log }_{\frac{1}{2}}3}=3$

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d)

$2^{2{\log }_{4}10}=4^{{\log }_{4}10}=10$

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e)

${25}^{{\log }_{5}2}=5^{2{\log }_{5}2}=5^{{\log }_5{2}^2}=2^2=4$

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f)

$8^{{\log }_{2}5}=2^{3{\log }_{2}5}=2^{{\log }_2{5}^3}=5^3=125$

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g)

$6^{{\log }_{6}4+1}=6\cdot 6^{{\log }_{6}4}=6\cdot 4=24$

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h)

$4^{{\log }_{4}3-2}=4^{-2}\cdot 2^{{\log }_{4}3}=\frac{1}{16}\cdot 3=\frac{3}{16}$