Question

Mi ajudem so a letra D,E,F

Answer 1

Para trabalhar esse tipo de problema (incógnita no expoente) usamos os logaritmos. (log ou ln)

d) $0,5^{x+1}=512$

$log0,5^{x+1}=log512$

$(x+1).log0,5=log512$

$x+1=\frac{log512}{log0,5}$

$x+1=-9$

$x=-9-1$

$x=-10$

e) $100^{x}=0,01$

$log100^x=log0,01$

$x.log100=log0,01$

$x=\frac{log0,01}{log100}$

$x=-1$

f) $\sqrt[3]{4^x} =8$

$4^{\frac{x}{3}}=8$

$log4^{\frac{x}{3}}=log8$

$\frac{x}{3}.log4=log8$

$\frac{x}{3}=\frac{log8}{log4}$

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

$x=\frac{3}{2} .3$

$x=\frac{9}{2}$