Question

me ajudem , urgente ... funçao exponencial

Answer 1

a) $(0,8)^{x}=\dfrac{5}{4}$

$0,8=\dfrac{8}{10}=\dfrac{4}{5}$

$\left(\dfrac{4}{5}\right)^{x}=\dfrac{5}{4}$

$\dfrac{5}{4}=\left(\dfrac{4}{5}\right)^{-1}$

$\left(\dfrac{4}{5}\right)^{x}=\left(\dfrac{4}{5}\right)^{-1}$

$x=-1$


b) $9^{x+1}=\sqrt[3]{3}$

$9^{x+1}=(3^2)^{x+1}=3^{2x+2}$

$\sqrt[3]{3}=3^{\frac{1}{3}$

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

$2x+2=\dfrac{1}{3}$

$6x+6=1$

$6x=-5$

$x=\dfrac{-5}{6}$


c) $5^{x+2}=125$

$5^{x+2}=5^3$

$x+2=3$

$x=1$


d) $\left(\dfrac{1}{4}\right)^{x}=\dfrac{1}{8}$

$\left(\dfrac{1}{4}\right)^{x}=(2^{-2})^{x}=2^{-2x}$

$\dfrac{1}{8}=2^{-3}$

$2^{-2x}=2^{-3}$

$-2x=-3$

$2x=3$

$x=\dfrac{3}{2}$


d) $27^{x}=9$

$(3^3)^{x}=3^2$

$3^{3x}=3^{2}$

$3x=2$

$x=\dfrac{2}{3}$