Question

URGENTE De o conjunto solução das seguintes equações

Answer 1

a)

$10^x~=~1000\\\\\\10^x~=~10^3\\\\\\10\!\!\!\backslash^x~=~10{\!\!\!\backslash}^3\\\\\\\boxed{x~=~3}$

b)

$(0,1)^{2x}~=~10\\\\\\\left(\frac{1}{10}\right)^{2x}~=~\left(\frac{1}{10}\right)^{-1}\\\\\\\left(\frac{1}{10}\!\!\!\!\backslash\right)^{2x}~=~\left(\frac{1}{10}\!\!\!\!\backslash\right)^{-1}\\\\\\2x~=~-1\\\\\\\boxed{x~=~-\frac{1}{2}}$

c)

$\left(0,001\right)^{x}~=~1000\\\\\\\left(\frac{1}{1000}\right)^{x}~=~\left(\frac{1}{1000}\right)^{-1}\\\\\\\left(\frac{1}{1000}\!\!\!\!\backslash\right)^{x}~=~\left(\frac{1}{1000}\!\!\!\!\backslash\right)^{-1}\\\\\\\boxed{x~=~-1}$

d)

$\left(\frac{1}{100}\right)^{2x}~=~0,0001\\\\\\\left(\frac{1}{100}\right)^{2x}~=~\frac{1}{10000}\\\\\\\left(\frac{1}{100}\right)^{2x}~=~\frac{1}{100^2}\\\\\\\left(\frac{1}{100}\right)^{2x}~=~\left(\frac{1}{100}\right)^2\\\\\\\left(\frac{1}{100}\!\!\!\!\backslash\right)^{2x}~=~\left(\frac{1}{100}\!\!\!\!\backslash\right)^2\\\\\\2x~=~2\\\\\\x~=~\frac{2}{2}\\\\\\\boxed{x~=~1}$