## Logarithms

Opposites are important in math.

The opposite of addition is subtraction. If x+4 = 5.5; Then x = 5.5 - 4

The opposite of multiplication is division. If x*4 = 6 Then x = 6/4

The opposite of an exponent is a logarithm. If 4

2

The two is called the base. Less importantly, the 6 is called the exponent and the 64 is the result.

log

The 3 is called the base. Less importantly the 81 is called the inside (or more technically, the argument), and the 4 is called the result.

The opposite of addition is subtraction. If x+4 = 5.5; Then x = 5.5 - 4

The opposite of multiplication is division. If x*4 = 6 Then x = 6/4

The opposite of an exponent is a logarithm. If 4

^{x}= 8, Then log_{4}8 = x2

^{6}= 64 is pronounced "two to the power six equals sixty-four"The two is called the base. Less importantly, the 6 is called the exponent and the 64 is the result.

log

_{3}81 = 4 is pronounced "log base three of eighty-one equals four"The 3 is called the base. Less importantly the 81 is called the inside (or more technically, the argument), and the 4 is called the result.

## Changing between Logarithmic and Exponential Equations

My first video explains how to change between logarithm and exponent forms of an equation when the base is on the left side. It is at http://www.youtube.com/watch?v=FgH9wZ3iQA8. My second video shows how to change between logarithmic and exponential equations when the base is on the right side (spoiler - you turn the equation around and then do the exact same thing as the first video) That video is at http://www.youtube.com/watch?v=N_Jpz0Eiiv8.

Example problems are done! Example answers aren't, though.

Example problems are done! Example answers aren't, though.

## Expanding and Contracting Logs

There are three basic formulas for expanding and contracting logs.

log(xy) = log(x) + log(y)

log(x/y) = log(x) - log(y)

log(x^n) = nlog(x)

log(xy) = log(x) + log(y)

log(x/y) = log(x) - log(y)

log(x^n) = nlog(x)