Question

$(\frac{3}{4})^{x+3}*\frac{4}{3}=\frac{\sqrt{3}}{2}$

Answer 1

Răspuns:

(3/4)ˣ⁺³*4/3=√3/2

(3/4)ˣ*(3/4)⁻1=√3/2

(3/4)ˣ⁻¹=√3/2=>

x-1=1/2

x=1/2+1

x=3/2

pas cu pas:

Answer 2

Explicație pas cu pas:

$(\frac{3}{4} )^{x+3}*\frac{4}{3} =\frac{\sqrt{3} }{2} \\(\frac{3}{4})^x*( \frac{3}{4})^3* \frac{4}{3} =\frac{\sqrt{3} }{2} \\\\(\frac{3}{4})^x*\frac{3^3}{4^3}* \frac{4}{3} =\frac{\sqrt{3} }{2} \\Simplificam~ 3^3~cu~3~si~4^3~cu~4.\\(\frac{3}{4})^x*\frac{3^2}{4^2}=\frac{\sqrt{3} }{2}\\Inmultim~ecuatia~cu~\frac{4^2}{3^2}.\\ (\frac{3}{4})^x=\frac{\sqrt{3} }{2}*\frac{4^2}{3^2}\\Scriem~pe~4^2~ca~(2^2)^2=2^4~si~3^2~ca~((\sqrt{3}) ^2)^2=(\sqrt{3})^4.$

$(\frac{3}{4})^x=\frac{\sqrt{3} }{2}*\frac{2^4}{(\sqrt{3})^4}\\ Simplificam.\\ (\frac{3}{4})^x=\frac{2^3}{(\sqrt{3})^3}\\\\Scriem~~3=(\sqrt{3} )^2~si~4=2^2.\\(\frac{(\sqrt{3} )^2}{2^2} )^x=(\frac{2}{\sqrt{3}})^3\\((\frac{\sqrt{3} }{2} )^2)^x=(\frac{2}{\sqrt{3}})^3\\(\frac{\sqrt{3} }{2} )^{2x}=(\frac{2}{\sqrt{3}})^3\\\\Functia~exponentiala ~este~injectiva.\\2x=-3\\x=-\frac{3}{2}$