เพิ่ม

ลด

คงที่

เพิ่ม

ลด

คงที่

เพิ่ม

ลด

คงที่

$$y=5^x$$

$$y=\left(\frac{1}{3}\right)^{-x}$$

$$y=\left(5\right)^{-x}$$

$$y=\left(\frac{1}{e}\right)^{-x}$$

$$\log_{\left(\frac{1}{2}\right)}x$$

$$\log_{\left(\frac{1}{3}\right)}\left(x^{-1}\right)$$

$$\log_3x$$

$$\frac{1}{2}\log_2x$$

$$y=\log_{\frac{1}{\pi}}x$$

$$y=\log_{\frac{1}{2}}x$$

$$y=\log_{\frac{4}{3}}x$$

$$y=\log_{\frac{1}{e}}x$$

$$\log_3243\ =\ 5$$

$$\log_5243\ =3$$

$$\log_{243}3\ =5$$

$$\log_35\ =243$$

$$4^2=16\ \leftrightarrow\ \log_416\ =\ 2$$

$$\log_{10}1000\ =3\ \leftrightarrow\ 10^3\ =1000$$

$$\left(\frac{1}{2}\right)^{-3}\ =8\ \ \leftrightarrow\ \log_{\frac{1}{2}}8\ =-3$$

$$\log_{0.1}0.001=3\leftrightarrow\ 0.1^{-3}=0.001\$$

$$\log_11$$

$$\log_e1$$

$$\log_{\left(-10\right)}1$$

$$\log_{10}10$$

$$\log_55$$

$$\log_11$$

$$\log_{\pi}\pi$$

$$\log_{0.0001}0.0001$$

$$7$$

12

81

64

$$\log_381+\log_39\ =\ \log_3\left(81\times9\right)$$

$$\log_{10}10\ +\log_{10}1000\ =\log_{10}\left(10\times1000\right)$$

$$\log_464\ +\log_416\ =\ \log_{16}\left(64\times16\right)$$

$$\log_5625-\log_525\ =\log_5\left(625\times25^{-1}\right)$$

$$\log_2\ \frac{64}{16}\ =\ \log_264\ -\log_216$$

$$\log_7343-\log_77\ =\log_7\ \ \frac{343}{7}$$

$$\log_{\left(\frac{1}{2}\right)}4-\log_{\left(\frac{1}{2}\right)}8\ =\log_{\frac{1}{2}}\ 4\times8$$

$$\log_aM\ -\log_aN\ =\ \log_{a\ }\ \frac{M}{N\ \ }\ ,\ a>0\ ,\ a\ne1\ M,N\in R^+$$

$$\log_xq+\log_xp+\log_xr\ =\log_xpqr$$

$$\log_x\left(p-q\right)+\log_x\left(p+q\right)\ =\log_x\left(p^2-q^2\right)$$

$$\log_axy^2-\left(\log_ax^2y^2-\log_axy\right)\ \ =\log_a\ \frac{\left(xy^2\right)\left(xy\right)}{x^2y^2}$$

$$\log_24-\left(\log_216-\log_28\right)\ =\ \log_2\ \frac{4}{16\times8}$$

$$\log_310^5\ =\ 5\log_310$$

$$\log_{2^4}5^3\ =\frac{3}{4}\log_25$$

$$\log_{\frac{1}{2}}\left(\frac{1}{4}\right)=2$$

$$\log_{3^2}\left(\frac{1}{9}\right)\ =1$$

5

10

$$256$$

20

-3

$$\frac{3}{2}$$

$$\frac{-3}{2}$$

3

$$\frac{5}{2}$$

$$\frac{2}{5}$$

$$\frac{-5}{2}$$

$$\frac{-2}{5}$$

$$\frac{18}{5}$$

$$\frac{18}{15}$$

$$\frac{27}{10}$$

$$\frac{5}{18}$$

7

2

$$7^2$$

$$2^7$$

5

25

49

$$\frac{1}{49}$$

$$\frac{y^{10}}{x^5}$$

$$\frac{x^5}{y^{10}}$$

$$\frac{10}{5}\log_xy$$

$$\frac{5}{10}\log_xy$$

35

625

1225

175

1

0

10

2

$$\frac{3}{2}$$

3

$$\frac{2}{3}$$

$$\frac{2}{3}$$

$$27$$

$$\frac{8}{4}$$

$$\frac{8}{3}$$

$$\frac{3}{8}$$

$$\log_{\frac{1}{10}\ }\ \frac{1}{100}=2$$

$$\log_{x^b}y^a\ =\frac{a}{b}\log_xy$$

$$\log_aM^p\ =\ \frac{1}{\frac{\log_{ }a}{p\log_{ }M}}$$

$$\log_x\ \left(\frac{1}{x}\right)\ =1$$