Question

Resolva essas questões exponenciais. Valendo 15 Pontos




a)5x².5^4=5^5x

b)7^2x-1=7^x.7^3

c)9^2x=27^x-4

d)2^x +2^x+3 -2^x-1=34

Me ajudem PFVR

Answer 1

a) $5^{x^2}\cdot5^{4}=5^{5x}$

$5^{x^2+4}=5^{5x}$

$x^2+4=5x$

$x^2-5x+4=0$

$\Delta=(-5)^2-4\cdot1\cdot4=25-16=9$

$x=\dfrac{-(-5)\pm\sqrt{9}}{2}=\dfrac{5\pm3}{2}$

$x'=\dfrac{5+3}{2}=\dfrac{8}{2}=4$

$x"=\dfrac{5-3}{2}=\dfrac{2}{2}=1$



b) $7^{2x-1}=7^{x}\cdot7^{3}$

$7^{2x-1}=7^{x+3}$

$2x-1=x+3$

$2x-x=3+1$

$x=4$



c) $9^{2x}=27^{x-4}$

$(3^2)^{2x}=(3^3)^{x-4}$

$3^{4x}=3^{3x-12}$

$4x=3x-12$

$4x-3x=-12$

$x=-12$



d) $2^{x}+2^{x+3}-2^{x-1}=34$

$2\cdot2^{x-1}+2^4\cdot2^{x-1}-1\cdot2^{x-1}=34$

$2^{x-1}\cdot(2+2^4-1)=34$

$2^{x-1}\cdot17=34$

$2^{x-1}=2$

$2^{x-1}=2^1$

$x-1=1$

$x=2$