Logs and Inverses

Hmmmmmm... Well what to say about Logs and Inverses.

There are so many things about these two topics.

Here is something i had a somewhat clear understanding of...

Logarithms: Logs first of all are... logx=10

First of all you would have to know that when there is "no" base or at least you can't see a base the base is 10.

So the problem would be the log base 10(x)=10...which means x equals 1.

ex.

log5(x)=125 making x=3

you can make it easier and say log base 5(x)=5^3, and that makes x=3.

ex.

log(xy)= log x + log y

Logs can also be described as natural log.

ex.

ln(x)=x, when the input equals 0.

Where is the base you ask..? the base is like in logs its invisible but its still there except for natural logs the base is "e"; "e" is a number like pi, which equals about 2.718.

-An exponential function is a function where we know the base and need to find out the exponent.

ex.

y=3^x

For this problem you would have to know what the x equals to find the outputs, the inputs are essy to find just plug in any number for x.

-A power function is a function where the x is the base.

ex.

y=x^2

y=x^3

I had a clearer understanding of inverses.

-An inverse is the same as an f(x) function but its f^-1(x).

For f(x) the input is x and the output =y.

For the inverse of f(x) the output would be considered the x and the input would equal the y.

They basically switch.

For an inverse to be a "one-to-one" it has to pass some tests.

The parent fucntion has to pass the vertical line test, and horizontal line test for the inverse to be a "one-to-one" function.

Some things I need help with is the same as most of my classmates...

how do we graph without the use of a calculator.

And the more complicated log functions...?