notes/education/math/Logarithms.md

https://www.youtube.com/watch?v=sULa9Lc4pck

log_a(b) 

Pronounced log base a, this function is used to figure out what exponent you need to raise a to to get b.

log_ab = c can be rewritten as a^c = b.

 5^{log_5^{(x+2)}}=x+2 

By default, log refers to log_{10}. ln is shorthand for log_e.

 \sqrt{x} = x^{1/2} 

To get the reciprocal of a value, change the sign of the exponent.

 x^{-1} = \frac{1}{x} 

Domain

There are 3 places you need to worry about domain.

• You can't divide by 0
• You can't take the square root of a negative without complex numbers
• You cannot take the log of a zero, or a negative number.
  • There's no way to raise a number to an exponent and have it equal zero, or be a negative number.
  • This can be used to help solve inequalities, because you know an equation that's wrapped in a logarithm must be > 0.

Adding logarithms

 log(x+2) + log(2x-3) 

With the above example, you can find the domain of each function separately, then find the overlap of valid numbers.