Logarithmic Properties

L2MAEL

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Using Log Properties:

Common Logs:

Before starting, it is essential to know that when the base of $\log$ is empty, the base is 10.

$$\log x={\log }_{10}x$$

This is just like how:

$$\sqrt[2]{x}=\sqrt{x}$$

Logging Numbers:

$\log$ging a number also works. You can log ANY positive numbers:

$$\log 2$$ $$\log 5$$

However, when you $\log$ a number, you must log the other side of the equation: $2=2$

$$\log 2=\log 2$$

Exponents:

When you log a number like $2^2$:

$$\log 2^2$$

The exponent can come down as a product:

$$2\times (\log 2)$$

In the calculator, $\log 2^2$ and $2\times (\log 2)$ will return the same result.

Log Rules:

$$\log a+\log b=\log ab$$ $$\log a-\log b=\log \frac{a}{b}$$ $${\log }_{a}b=\frac{\log b}{\log a}$$