Question

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Answer 1

Verified answer

Odpowiedź:

a )[tex]3^{log_3 8} = 8[/tex]

[tex]0,5^{log_{0,5} 5 = 5[/tex]

[tex](\sqrt{2})^{log_{\sqrt{2}} 3 = 3[/tex]

[tex]e^{ln 12} = 12[/tex]

b )  

[tex]5^{2log_57} = 5^{log_5 7^2} = 7^2 = 49[/tex]

[tex]10^{3 log 5} = 10^{log 5^3} = 5^3 = 125[/tex]

[tex]6^{2 log_6 10} = 6^{log_6 10^2} = 10^2 = 100[/tex]

[tex]e^{2 ln 5} = e^{ln 5^2} = 5^2 = 25[/tex]

c)  [tex]25^{log_5 2} = ( 5^2)^{log_5 2} = 5^{2 log_5 2} = 5^{ log_5 2^2} = 2^2 = 4[/tex]

d ) [tex]8^{log_2 5} = (2^3)^{log_2 5} = 2^{3log_2 5} =2^{log_2 5^3} = 5^3 = 125[/tex]

e ) [tex]7^{2 log_7 3 + 1 } = 7*7^{2 log_73 } =7*7^{log_7 3^2} =7*9 = 63[/tex]

f ) [tex]3^{4 log_3 5 - 3} = 3^{-3}*log_3 5^4} = \frac{1}{27}*625 = \frac{625}{27}[/tex]

g )  [tex]27^{2 log_3 2 - 1} = 27^{-1}*( 3^3)^{2 log_3 2} = \frac{1}{27} *3^{6 log_3 2} =\frac{1}{27} *3^{log_3 2^6} = \frac{1}{27} *2^6 = \frac{64}{27}[/tex]

Wyjaśnienie:

[tex]a^{log_a x} = x[/tex]

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