Question

!!URGENTE!!
Equação exponencial:
A- 10.5(elevado a x+3)=10
B- 16(elevado a 3x+1)=64(elevado a x-4)
C- 625(elevado a 2x-1)=125
D- 4(elevado a -4x-1)=128

Answer 1

a) $10\cdot5^{x+3}=10$

$5^{x+3}=\dfrac{10}{10} \iff 5^{x+3}=1 \iff 5^{x+3}=5^{0}$

Igualando os expoentes:

$x+3=0 \iff \boxed{x=-3}$


b) $16^{3x+1}=64^{x-4}$

Note que $16=2^4$ e $64=2^6$:

$(2^4)^{3x+1}=(2^6)^{x-4} \iff 2^{12x+4}=2^{6x-24}$

Igualando os expoentes:

$12x+4=6x-24 \iff 6x=-28 \iff x=\dfrac{-28}{6} \iff \boxed{x=-\dfrac{14}{3}}$


c) $625^{2x-1}=125$

Veja que $625=5^{4}$ e $125=5^3$

$(5^4)^{2x-1}=5^3 \iff 5^{8x-4}=5^3$

$8x-4=3 \iff 8x=7 \iff \boxed{x=\dfrac{7}{8}}$


d) $4^{-4x-1}=128$

Observe que $4=2^2$ e $128=2^7$

$(2^2)^{-4x-1}=2^7 \iff 2^{-8x-2}=2^7$

Igualando os expoentes:

$-8x-2=7 \iff -8x=9 \iff \boxed{x=-\dfrac{9}{8}}$