Question

Resolva os logaritmos: 1° Log 1/8 = x 1024     2 ° Log 7 = x 2401      3° Log 1/25 = x 625     4° Log 25 = x 3125         5° Log 1 = x

Answer 1

1 - Log1/8 1024 = x

 

$<var>\frac{1}{8}^{x} =1024\\2^{-3x} = 2^{10}\\-3x=10\\x=\frac{-10}{3} </var>$

 

2 - Log7 2041 = x

$<var>7^{x}=2041\\7^{x}=7^{4}\\x=4</var>$

 

3- Log 1/25 625 = x

 

$<var>\frac{1}{25}^{x}=625\\5^{-2x}=5^{4}\\-2x=4\\x=-2</var>$

 

4- Log 25 3125 = x 

 

$<var>25^{x}=3125\\5^{2x}=5^{5}\\2x=5\\x=\frac{5}{2}</var>$

 

5-  Log 1 = x (mesma coisa que Log10 1 = x) 

 

$<var>10^{x}=1\\10^{x}=10^{0}\\x=0</var>$

Answer 2

a)

$\text{log}~1024=\text{x}$

$\dfrac{1}{8}^{\text{x}}=1~024$

Como $\dfrac{1}{8}=2^{-3}~\wedge~1~024=2^{10}$, segue que:

$2^{-3\text{x}}=2^{10}$

Donde, obtemos:

$-3\text{x}=10$

$\text{x}=-\dfrac{10}{3}$