How does the log(x) function work?

[Vegitto]

Hey.

Yesterday, in math class, I was presented with a solution for my problem by my math teacher. The problem was: a^x=r. How to get x?

His solution was x=((log(r))/(log(a)))
My question, how does this function work?

 

[hypn0tik]

Originally posted by: Vegitto
Hey.

Yesterday, in math class, I was presented with a solution for my problem by my math teacher. The problem was: a^x=r. How to get x?

His solution was x=((log(r))/(log(a)))
My question, how does this function work?

If you have the expression: log_a (b) = c (where a is a subscript while b is not), it is defined as:

a^c = b.

Essentially, it reads as "c is the exponent you have to put on a to get b"

 

[LordMorpheus]

Originally posted by: hypn0tik

Originally posted by: Vegitto
Hey.

Yesterday, in math class, I was presented with a solution for my problem by my math teacher. The problem was: a^x=r. How to get x?

His solution was x=((log(r))/(log(a)))
My question, how does this function work?

If you have the expression: log_a (b) = c (where a is a subscript while b is not), it is defined as:

a^c = b.

Essentially, it reads as "c is the exponent you have to put on a to get b"

To further clarify this answer, log_a(b) can be written as log(b)/log(a), where those logs could be base anything. To get a natural log using only base ten logs, you could say ln(b) = log(b)/log(e).

 

[hypn0tik]

Originally posted by: LordMorpheus

Originally posted by: hypn0tik

Originally posted by: Vegitto
Hey.

Yesterday, in math class, I was presented with a solution for my problem by my math teacher. The problem was: a^x=r. How to get x?

His solution was x=((log(r))/(log(a)))
My question, how does this function work?

If you have the expression: log_a (b) = c (where a is a subscript while b is not), it is defined as:

a^c = b.

Essentially, it reads as "c is the exponent you have to put on a to get b"

To further clarify this answer, log_a(b) can be written as log(b)/log(a), where those logs could be base anything. To get a natural log using only base ten logs, you could say ln(b) = log(b)/log(e).

Good point. Switching bases when using logarithms can prove to be useful in certain situations.

It would help immensely if you familiarize yourself with the properties of logarithms and know where they come from.

 

[Vegitto]

Originally posted by: hypn0tik

Originally posted by: LordMorpheus

Originally posted by: hypn0tik

Originally posted by: Vegitto
Hey.

Yesterday, in math class, I was presented with a solution for my problem by my math teacher. The problem was: a^x=r. How to get x?

His solution was x=((log(r))/(log(a)))
My question, how does this function work?

If you have the expression: log_a (b) = c (where a is a subscript while b is not), it is defined as:

a^c = b.

Essentially, it reads as "c is the exponent you have to put on a to get b"

To further clarify this answer, log_a(b) can be written as log(b)/log(a), where those logs could be base anything. To get a natural log using only base ten logs, you could say ln(b) = log(b)/log(e).

Good point. Switching bases when using logarithms can prove to be useful in certain situations.

It would help immensely if you familiarize yourself with the properties of logarithms and know where they come from.

Yeah, I understood what it meant. The question is actually, how does the calculator know that 10^x=1000, x=3?

 

[Special K]

Originally posted by: Vegitto

Originally posted by: hypn0tik

Originally posted by: LordMorpheus

Originally posted by: hypn0tik

Originally posted by: Vegitto
Hey.

Yesterday, in math class, I was presented with a solution for my problem by my math teacher. The problem was: a^x=r. How to get x?

His solution was x=((log(r))/(log(a)))
My question, how does this function work?

If you have the expression: log_a (b) = c (where a is a subscript while b is not), it is defined as:

a^c = b.

Essentially, it reads as "c is the exponent you have to put on a to get b"

To further clarify this answer, log_a(b) can be written as log(b)/log(a), where those logs could be base anything. To get a natural log using only base ten logs, you could say ln(b) = log(b)/log(e).

Good point. Switching bases when using logarithms can prove to be useful in certain situations.

It would help immensely if you familiarize yourself with the properties of logarithms and know where they come from.

Yeah, I understood what it meant. The question is actually, how does the calculator know that 10^x=1000, x=3?

log(x) can be expressed as a power series - an infinite summation of terms. Add enough of these terms together, and you can calculate log(x) (as well as trig functions) to any desired precision.

There is also the CORDIC algorithm. I am only familiar with its use in calculating trig functions but I remember reading it can be used for logarithms as well. In calculating trig functions it uses a binary search method to "search out" the answer. I would imagine it does something similar for logs.