$$y=a^x$$
$$y=log_{a}x$$
$$y=a^x\;\;$$$$и$$$$\;\;\:y=log_{a}x$$
$$a^{x+z} = a^{x} \cdot a^{z};\quad$$ $$a^{x-z} = \frac{a^{x}}{a^{z}};$$
$$\left(a^{x}\right)^{z} = a^{x\cdot z} = \left(a^{z}\right)^{x};\;$$
$$(a\cdot b)^x = a^x \cdot b^x;\quad$$ $$\left(\frac{a}{b}\right)^x = \frac{a^x}{b^x};$$
$$a^0 = 1;\quad$$ $$a^{-x} = \frac{1}{a^x};\quad$$ $$\sqrt[n]{a^x} = a^{\frac{x}{n}};$$
Если $$\;\;a^{x} = a^{z},\;\;$$ то $$\;\;x=z;$$
$$lg{x}=log_{_{10}}{x};\quad$$ $$ln{x}=log_{e}{x};$$
$$log_{a}{a}=1;\quad$$ $$a^{log_{a}{x}}=x;\quad$$ $$log_{a}{1}=0;$$
$$log_{a}{x^p}=p\cdot log_{a}{x};\quad$$ $$log_{a^q}{x}=\frac{1}{q}\cdot log_{a}{x};$$
$$log_{a}{b}=\frac{log_{c}{b}}{log_{c}{a}};\quad$$ $$log_{a}{x}=\frac{1}{log_{x}{a}};$$
$$log_{a}{(x\cdot z)}=$$$$\;log_{a}{x}+log_{a}{z};$$
$$log_{a}{\left (\frac{x}{z} \right)} =$$$$\;log_{a}{x}-log_{a}{z};$$