Question

Resolva as equações
3^x+1=27
0,25^2x+3=4^x-1
√7^x=343
5^3/2x=125^4
6^√1000.10^x=0,0001
(8^x)/2^x+2=256

Answer 1

$3^{(x+1)}=27 \rightarrow 3^{(x+1)}=3^3 \rightarrow x+1=3 \rightarrow \boxed{x=2}$

$0,25^{(2x+3)}=4^{(x-1)}\rightarrow 4^{-2x-3}=4^{x-1} \rightarrow -2x-3=x-1\rightarrow \boxed{x=\frac{2}{3}}$

$\sqrt{7^x}=343 \rightarrow 7^{\frac{x}{2}}=7^3 \rightarrow \dfrac{x}{2}=3 \rightarrow \boxed{x=6}$

$5^{(3/2)x}=125^4 \rightarrow 5^{\frac{3x}{2}}=(5^3)^4\rightarrow \dfrac{3x}{2}=12 \rightarrow \boxed{x=8}$

$\dfrac{8^x}{2^{x+2}}=256 \rightarrow 2^{3x}.2^{-x-2}=2^8 \rightarrow 3x-x-2=8 \rightarrow \boxed{x=5}$