Question

Oblicz Logarytmy proszę o pomoc to na jutro

Answer 1

a)

[tex] log_{5}(25) \\ {5}^{?} = 25 \\ {5}^{2} = 25 \\ log_{5}(25) = 2[/tex]

b)

[tex]3 log_{4}(16) \\ 3 log_{4}( {4}^{2} ) \\ 3 \times 2 = 6 \\ 3 log_{4}(16) = 6[/tex]

c)

[tex]4 log_{5}(125) \\ 4 log_{5}( {5}^{3} ) \\ 4 \times 3 = 12 \\ 4 log_{5}(125) = 12[/tex]

d)

[tex] \frac{1}{3} log_{3}(27) \\ \frac{1}{3} log_{3}( {3}^{3} ) \\ \frac{1}{3} \times 3 = 1 \\ \frac{1}{3} log_{3}(27) = 1[/tex]

e)

[tex] log_{9}(81) + log_{9}(9) \\ log_{9}( {9}^{2} ) + 1 \\ 2 + 1 = 3 \\ log_{9}(81) + log_{9}(9) = 3[/tex]

f)

[tex] log_{9}(81) - log_{9}(9) \\ log_{9}( {9}^{2} ) - 1 \\ 2 - 1 = 1[/tex]

g)

[tex] log_{5}( {25}^{3} ) \\ {5}^{?} = {25}^{3} \\ {5}^{6} = {25}^{3} \\ log_{5}( {25}^{3} ) = 6[/tex]

h)

[tex] log_{2}(8) - log_{2}(4) \\ log_{2}( {2}^{3} ) - log_{2}( {2}^{2} ) \\ 3 - 2 = 1[/tex]

i)

[tex] log_{5}( \frac{1}{5} ) \\ {5}^{?} = \frac{1}{5} \\ {5}^{ - 1} = \frac{1}{5} \\ log_{5}( \frac{1}{5} ) = - 1[/tex]

j)

[tex] log_{ \frac{1}{7} }(7) \\ ({ \frac{1}{7} )}^{?} = 7 \\ ( { \frac{1}{7}) }^{ - 1} = 7 \\ log_{ \frac{1}{7} }(7) = - 1[/tex]

k)

[tex] log_{6}( \frac{1}{36} ) \\ {6}^{?} = \frac{1}{36} \\ {6}^{ - 2} = \frac{1}{36} \\ log_{6}( \frac{1}{36} ) = - 2[/tex]

l)

[tex] - 2 \times log_{3}( \frac{1}{9} ) \\ - 2 \times log_{3}( {3}^{ - 2} ) \\ - 2 \times ( - 2) = 4[/tex]

m)

[tex]5 \times log_{10}(100) + \frac{1}{2} \times log_{10}(10000) \\ 5 \times log_{10}( {10}^{2} ) + \frac{1}{2} \times log_{10}( {10}^{4} ) \\ 5 \times 2 + \frac{1}{2} \times log_{10}( {10}^{4 \\ } ) \\ 5 \times 2 + \frac{1}{2} \times 4 \\ 5 \times 2 + 2 = 12[/tex]