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:

a) 8

b) -2

c) 3

d) -4

e) 4

f) 7/8

g 4/3

h) 1

i) 3

$a) \: log_{2}(256) \\ log_{2}( {2}^{8}) \\ 8 \\ \\ b) \: log_{7}( \frac{1}{49}) \\ log_{7}( {7}^{ - 2}) \\ - 2 \\ \\ c) \: log_{ \frac{5}{2} }( \frac{125}{8} ) \\ log_{ \frac{5}{2} }( \frac{5}{2} )^{3} \\ 3 \\ \\ d) \: log_{ \frac{3}{2} }( \frac{16}{81}) \\ log_{ \frac{3}{2} }( \frac{2}{3})^{4} \\ log_{ \frac{3}{2} }( \frac{3}{2}) ^{ - 4} \\ - 4 \\ \\ e) \: log(10000) \\ log( {10}^{4}) \\ 4 \\ \\ f) \: log_{256}(128) \\ log_{ {2}^{8} }( {2}^{7}) \\ log_{2}( {2}^{ \frac{7}{8} } ) \\ \frac{7}{8} \\ \\ g) \: log_{ \frac{8}{27} }( \frac{16}{81} ) \\ log_{( \frac{2}{3} {)}^{3} }( \frac{2}{3} {}^{} ) {}^{4} \\ log_{ (\frac{2}{3}) }( \frac{2}{3} ) {4}^{3} \\ \frac{4}{3} \\ \\ h) \: log( \sqrt[5]{100} ) \\ log(100 {}^{ \frac{1}{2} }) \\ log(10 {}^{2 \times \frac{1}{2} } ) \\ 1 \\ \\ i) \: log_{0.5}(0.125) \\ log_{ \frac{1}{2} }( \frac{125}{1000} ) \\ log_{ \frac{1}{2} }( \frac{5}{10}) {}^{3} \\ log_{ \frac{1}{2} }( \frac{1}{2}) {}^{3} \\ 3$

Espero ter ajudado! ✌

Bons estudos! ☺