Question

Função exponencial.
a) 9^x = 243
b) (1/4)^4x = 0,25
c) 4^x = raiz cubica de 32
d) (5/3)^2x = 27/125
e) 10^3x = 1/100

Answer 1

a)
$9^{x} = 243 \\ \\ 3^{2x} = 3^{5} \\ \\ 2x = 5 \\ \\ x = \frac{5}{2}$
b)

$( \frac{1}{4} )^{4x} = 0.25 \\ \\ ( \frac{1}{4} )^{4x} = \frac{1}{?} \\ \\ ( \frac{1}{4} )^{4x} = ( \frac{1}{4} )^{1} \\ \\ 4x = 1 \\ \\ x = \frac{1}{4}$
c)

$4 ^{x} = \sqrt[3]{32} \\ \\ 2^{2x} = 2^{ \frac{5}{3} } \\ \\ 2x = \frac{5}{3} \\ \\ x = \frac{5}{6}$
d)

$( \frac{5}{3} )^{2x} = \frac{27}{125} \\ \\ ( \frac{5}{3} ) = ( \frac{5}{3} ) ^{ - 3} \\ \\ 2x = - 3 \\ \\ x = - \frac{3}{2}$
E)

$10 ^{3x} = \frac{1}{100} \\ \\ 10 ^{3x} = 10^{ - 2} \\ \\ 3x = - 2 \\ \\ x = - \frac{ 2}{3}$