6-1 Logarithms and Logarithmic Functions

$$16\ =\ 4^2$$

$$4\ =16^2$$

$$4\ =\ 16^2$$

$$2^2\ =\ 4$$

$$3\ =\ 729^6$$

$$729\ =\ 3^6$$

$$6\ =\ 3^{729}$$

$$3^6\ =\ 729$$

$$8\ =512\ ^3$$

$$8\ =\ 512^3$$

$$512\ =8^2$$

$$512\ =8^3$$

$$5\ =\ 625^2$$

$$625\ =\ 5^4$$

$$5\ =\ 625^4$$

$$625\ =\ 5^2$$

$$\log_4\ 64\ =3$$

$$\log_{64}\ 4\ =3$$

$$\log_3\ 4\ =3$$

$$\log_{64}\ 3\ =4$$

$$\log_5\ \frac{1}{3}\ =5$$

$$\log_5\ 125\ =\frac{1}{3}$$

$$\log_{125}\ 5\ =\frac{1}{3}$$

$$\log^{\frac{1}{3}}\ 125\ =\ 5$$

$$\log_3\ 11\ =1331$$

$$\log_{1331}\ =11$$

$$\log_{1331}\ 3\ =11$$

$$\log_{11}1331\ =3$$

$$\log^{\frac{3}{4}}\ 8\ =16$$

$$\log_8\ \frac{3}{4}\ =16$$

$$\log_{16\ }8=\frac{3}{4}$$

$$\log_8\ 16\ =\frac{3}{4}$$

-4/1

4

-4

-1

1/2

-2

4

2