Question

1) Calcule os logaritmos.
a) log$_{2}$ 256
b) log$_{7}$ $\frac{1}{49}$
c) log5/2 $\frac{125}{8}$
d) log3/2 $\frac{16}{81}$
e) log 10.000
f) log$_{256}$ 128
g) log8/27 $\frac{16}{81}$
h) log $\sqrt[5]{100}$
i) log$_{0,5}$ 0,125

Answer 1

Resposta:

$\textsf{Leia abaixo}$

Explicação passo a passo:

$\mathsf{a)\:log_2\:256 = log_2\:2^8 = 8}$

$\mathsf{b)\:log_7\:\dfrac{1}{49} = log_7\:7^{-2} = -2}$

$\mathsf{c)\:log_{\frac{5}{2}}\:\dfrac{125}{8} = log_{\frac{5}{2}}\left(\dfrac{5}{2}\right)^3 = 3}$

$\mathsf{d)\:log_{\frac{3}{2}}\:\dfrac{16}{81} = log_{\frac{3}{2}}\left(\dfrac{3}{2}\right)^{-4} = -4}$

$\mathsf{e)\:log\:10.000= log\:10^4 = 4}$

$\mathsf{f)\:log_{256}\:128 = log_{2^8}\:2^7 = \dfrac{7}{8}\:.\:log_2\:2 = \dfrac{7}{8}}$

$\mathsf{g)\:log_{\frac{8}{27}}\:\dfrac{16}{81} = log_{\frac{2^3}{3^3}}\left(\dfrac{2}{3}\right)^{4} = \dfrac{4}{3}\:.\:log_{\frac{2}{3}}\:\dfrac{2}{3} = \dfrac{4}{3}}$

$\mathsf{h)\:log\:\sqrt[5]{100} = log\:10^{\frac{2}{5}} = \dfrac{2}{5}}$

$\mathsf{i)\:log_{0,5}\:0,125 = log_{0,5}\:(0,5)^3 = 3}$

Answer 2

Explicação passo-a-passo:

A)

$log_{2}(256)$

$log_{2}(2 {}^{8} )$

8

B)

$log_{7}( \dfrac{1}{49} )$

$log_{7}(7 {}^{ - 2} )$

-2

C)

$log_{ \frac{5}{2} }( \dfrac{125}{8} )$

$log_{ \frac{5}{2} }(( \dfrac{5}{2} ) {}^{3} )$

3

D)

$log_{ \frac{3}{2} }( \dfrac{16}{81} )$

$log_{ \frac{3}{2} }(( \dfrac{3}{2}) {}^{ - 4} )$

-4

E)

$log_{10}(10000)$

$log_{10}(10 {}^{4} )$

4

F)

$log_{256}(128)$

$log_{2 {}^{7} }(2 {}^{8} )$

7/8

G)

$log_{ \frac{8}{27} }( \dfrac{16}{81} )$

$log_{( \frac{2}{3}) {}^{3} }(( \dfrac{2}{3}) {}^{4} )$

4/3

H)

$log_{10}( \sqrt[5]{100} )$

$log_{10}(10 {}^{ \frac{2}{5} } )$

2/5

I)

$log_{0.5}(0.125)$

$log_{2 {}^{ - 1} }(2 {}^{ - 3} )$

3