Question

Resolva as seguintes equaçoes exponenciais.
Me ajuda ae galera

Answer 1

e)
$125^{x+2}=1 \\ 5^{3(x+2)=5^0$
$3(x+2)=0 \\ 3x+6=0 \\ 3x=-6 \\ x=-6\div3 \\ x=-2$

f)
$8^{x+2}=16^{x-1} \\ 2^{3(x+2)}=2^{4(x-1)} \\ 3(x+2)=4(x-1) \\ 3x+6=4x-4 \\ 3x-4x=-4-6 \\ -x=-10 \\ x=10$

g)
$3^{4(6+x)}=3^{2(-2x)} \\ 4(6+x)=2(-2x) \\ 24+4x=-4x \\ 4x+4x=-24 \\ 8x=-24 \\ x=-24\div8 \\ x=-3$

h)
$2^{x+1}=2^5 \\ x+1=5 \\ x=5-1 \\ x=4$

i)
$5^x+5^{x+1}=30 \\ \\ 5^x+5^x.5=30 \\ 5^x(1+5)=30 \\ 5^x.6=30 \\ 5^x=30\div6 \\ 5^x=5 \\ x=1$

j)
$2^{x-3}+2^x=9 \\ 2^x.2^{-3}+2^x=9 \\ 2^x(2^{-3}+1)=9 \\ 2^x( \frac{1}{8} +1)=9 \\ \\ 2^x( \frac{9}{8})=9 \\ \\ 2^x=9. \frac{8}{9} \\ \\ 2^x=8 \\ 2^x=2^3 \\ x=3$