Question

помогите пожалуйста ​

Answer 1

1)

$2^x=16\\2^x=2^4\\x=4$

2)

$0.5^x=0.125\\0.5^x=0.5^3\\x=3$

3)

$4^x=\dfrac{1}{16}\\\\4^x=\dfrac{1}{4^2}\\\\4^x=4^{-2}\\x=-2$

4)

$\left(\dfrac{1}{6}\right)^x=36\\\\\dfrac{1}{6^x}=36\\\\6^x=\dfrac{1}{36}\\\\6^x=\dfrac{1}{6^2}\\\\6^x=6^{-2}\\x=-2$

5)

$10^x=\sqrt[3]{100}\\10^x=10^{\frac{1}{3}}\\x=\dfrac{1}{3}$

6)

$0.3^x=\dfrac{1000}{27}\\\\0.3^x=\dfrac{1}{0.027}\\\\0.3^x=\dfrac{1}{0.3^3}\\\\0.3^x=0.3^{-3}\\x=-3$

7)

$5^x=\dfrac{1}{\sqrt[3]{25}}\\\\5^x=\dfrac{1}{25^{\frac{1}{3}}}\\\\5^x=\dfrac{1}{(5^2)^{\frac{1}{3}}}\\\\5^x=\dfrac{1}{5^{\frac{2}{3}}}\\\\5^x=5^{-\frac{2}{3}}\\\\x=-\dfrac{2}{3}$

8)

$2^{x+1}=4\\2^{x+1}=2^2\\x+1=2\\x=1$

9)

$3^{-1-x}=\left(\dfrac{1}{3}\right)^{2x+3}\\\\(3^{-1})^{-1-x}=(3^{-1})^{2x+3}\\-1-x=2x+3\\-3x=4\\x=-\dfrac{4}{3}$

10)

$6^{2x-8}=216^x\\6^{2x-8}=(6^3)^x\\6^{2x-8}=6^{3x}\\2x-8=3x\\-8=x\\x=-8$

11)

$3^{x^2-4.5}\cdot\sqrt3=\dfrac{1}{27}\\\\3^{x^2-4.5}\cdot3^\frac{1}{2}=\dfrac{1}{3^3}\\\\3^{x^2-4.5+0.5}=3^{-3}\\x^2-4=-3\\x^2=1\\x=\pm1$