Question

1) Resolva as equações exponenciais:

a) 3 ^x + 1 = 9
b) 5 ^2x – 2 = 25
c) 4 ^x = 2^4
d) 2 ^x + 1 = 8

Answer 1

Ok , vamos lá !!

Resoluções :

A )

$\sf { {3}^{x} + 1 = 9}$

$\sf { {3}^{x} + 1 = {3}^{2} }$

$\sf {x + 1 = 2}$

$\sf {x = 2 - 1}$

$\red{\sf {x = 1}}$

B )

$\sf { {5}^{2x} - 2 = 25}$

$\sf { {5}^{2x} - 2 = {5}^{2} }$

$\sf {2x - 2 = 2}$

$\sf {2x = 2 + 2}$

$\sf {2x = 4}$

$\sf {x = \dfrac{4}{2} }$

$\sf {\red{x = 2}}$

C )

$\sf { {4}^{x} = {2}^{4} }$

${4}^{{x} } = 16$

$\sf {{4}^{{x} } = {4}^{2} }$

$\sf {\red{x = 2}}$

D )

$\sf { {2}^{x} + 1 = 8}$

$\sf { {2}^{x} + 1 = {2}^{3} }$

$\sf {x + 1 = 3}$

$\sf {x = 3 - 1}$

$\sf {\red{x = 2}}$

Bons estudos .