Question

1.Resolva as seguintes equações:
x 2x 1-3x
A) 2 =64 F) (0,5) =2

x-2 2-x
B)3 =9 G) 3 =1
27
2
x -2x x
C)5 =125 H)10 =0,000001

1-x x
D)10 = 1 I) 1 =8
10 32

x x
E)(√2) =4 J) 4 =16

Answer 1

$A) 2^x=64\to 2^x=2^6\to x=6\\\\ B) 3^{x-2}=9\to 3^{x-2}=3^2\to x-2=2\to x=4\\\\ C) 5^{x^2-2x}=125\to 5^{x^2-2x}=5^3\to x^2-2x=3\\ x^2-2x-3=0\\\\\Delta=(-2)^2-4\cdot(1)\cdot(-3)\\\Delta=4+12\\\Delta=16\\\\x=\frac{-(-2)\pm\sqrt16}{2\cdot1}\to x=\frac{2\pm4}{2}\\\\x'=\frac{2+4}{2}=3\\\\x''=\frac{2-4}{2}=-1\\\\ D) 10^{1-x}=\frac{1}{10}\to 10^{1-x}=10^{-1}\to 1-x=-1\to x=2\\\\ E) (\sqrt2)^x=4\to (2^{\frac{1}{2}})^x=2^2\to 2^{\frac{x}{2}}=2^2\to \frac{x}{2}=2\to x=4$$\\\\F) (0,5)^{2x}=2^{1-3x}\to (\frac{1}{2})^{2x}=2^{1-3x}\to (2^{-1})^{2x}=2^{1-3x}\\ -2x=1-3x\to -2x+3x=1\to x=1\\\\ G) 3^{2-x}=\frac{1}{27}\to 3^{2-x}=\frac{1}{3^3}\to 3^{2-x}=3^{-3}\to 2-x=-3\\-x=-3-2\to x=5\\\\ H) 10^x=0,000001\to 10^x=\frac{1}{10^6}\to 10^x=10^{-6}\to x=-6\\\\ I) \frac{1}{32}=8^x\to \frac{1}{2^5}=(2^3)^x\to 2^{-5}=2^{3x}\to -5=3x\to x=-\frac{5}{3}\\\\J) 4^x=16\to 4^x=4^2\to x=2$