Question

resolva as seguintes equação (a) 5^x=125. (b) 3^x+1=243. (c) 2^x=512^2. (d) 25^x=625

Answer 1

$a)~~~5^x=125\to~~\not5^x=\not5^3\to~~\boxed{x=3}\\\\\\ b)~~~3^{x+1} = 243\to~~ \not3^{x+1}=\not^5\to~~ x+1=5\to~~x=5-1\to~~\boxed{x=4} \\\\\\ c)~~~2^x=512^2\to~~ \not2^x=\not2^{9.2}\to~~ x=9.2\to~~ \boxed{x=18}\\\\\\d)~~~25^x=625\to~~ \not5^{2.x}=\not5^4\to~~ 2x=4\to~~x= \dfrac{4}{2} \to~~ \boxed{x=2}$

Answer 2

Regra:
Deixar na mesma base e simplificar.
Sobram-se os expoentes.
Isolar "x"

a)

     x
5        =   125

   x           3
5      =   5

x = 3
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b) 3^x+1=243.      
   
     x + 1             5
3             =   3

x + 1 = 5
x = 5 - 1
x = 4

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(c) 2^x=512^2

     x               2
2       =  512

   x       [    9 ] 2
2      =  [2    ]

x = 9.2
x = 18

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(d)
25^x=625

       x            2
25      =  25

x = 2