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

Vamos là.

a) log2(256) = log2(2^8) = 8log2(2) = 8

b) log7(1/49) = log7(7^-2) = -2log7(7) = -2

c) log5/2 (125/8) = log5/2 ((5/2)^3) = 3

d) log3/2 (16/81) = -log3/2 (81/16) = -log3/2 ((3/2)^4) = -4

e) log(10000) = 4

f) log256(128) = log2(128)/log2(256) = 7/8

g) log8/27 (16/81) = log( (2/3)^4) / log( (2/3)^3) = 4/3  

h) log(⁵√100) = 2/5

i) log0,5(0,125) = log0,5(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