# Why is there a twist in these logarithms?

• sidt36
In summary, the conversation involves a problem that has been puzzling the individual for a week. They discuss the equation (log_b(a)log_c(a) + log_a(a)) + (log_a(b)log_c(b) + log_b(b)) + (log_a(c)log_b(c) + log_c(c)) = 0 and the goal of proving that abc = 1. They also mention trying to convert to a common log base and using the formula a3 + b3 + c3 = 3abc. The individual eventually solves the problem on their own.
sidt36
MENTOR note: THread moved from General Math

I just can get it

This problem has been driving me crazy for a week now

$$If\quad a,b,c\quad \neq \quad 1\\ Also\quad (log_{ b }{ a\cdot }log_{ c }{ a }\quad +\quad log_{ a }{ a })\quad +\quad (log_{ a }{ b\cdot }log_{ c }{ b }\quad +\quad log_{ b }{ b })\quad +\quad (log_{ a }{ c\cdot }log_{ b }{ c }\quad +\quad log_{ c }{ c })\quad =\quad 0\\ Prove\quad that\quad \\ abc\quad =\quad 1\\ Additionally\\ If\quad a,b,c\quad =\quad 1\quad Prove\quad a=b=c$$My attempt

So what I did was

call log_a b = p ,log_b = q,log_c a=q

I plugged this in and made an interesting discovery

pqr = 1

So i used this in the equation above and tried to get to the proof but didn't work

Where am I faltering
?

On the first proof, did you notice how to simplify the ##log_{a} ( a )##?

Of course i wrote it as 1 and proceeded

Did you try to convert the factors to a common log base base like log_b(a) + ln(a)/ln(b)?

Yes i did try that

and will you be showing your work? We can't help you here unless you show some work.

Well its alright i got it on my own

jedishrfu
so what was the trick you needed?

I needed to remember that If a3 + b3 + c3 = 3abc

a+b+c=0 or a=b=c

sidt36 said:
I needed to remember that If a3 + b3 + c3 = 3abc

a+b+c=0 or a=b=c

Where did that come from? It wasn't part of the original problem you posted.

sidt36 said:
I needed to remember that If a3 + b3 + c3 = 3abc

## 1. What is a logarithm with a twist?

A logarithm with a twist is a mathematical concept that involves taking the logarithm of a number to a base that is not a commonly used number, such as the natural logarithm or base 10. This can lead to unique and unexpected results.

## 2. How is a logarithm with a twist different from a regular logarithm?

A regular logarithm is typically calculated with a base of 10 or the natural logarithm, and is used to find the exponent needed to produce a certain number. A logarithm with a twist uses a different base, which can lead to different results.

## 3. Can you give an example of a logarithm with a twist?

Sure, an example of a logarithm with a twist is taking the base 2 logarithm of 8. This is written as log28 and results in a value of 3, since 2 to the power of 3 equals 8.

## 4. What is the purpose of using a logarithm with a twist?

The purpose of using a logarithm with a twist is to explore alternative mathematical concepts and gain a deeper understanding of logarithms. It can also be used in certain applications, such as cryptography and data compression.

## 5. Are there any real-world applications of logarithms with a twist?

Yes, logarithms with a twist have various applications in fields such as computer science, physics, and engineering. They can be used to solve complex problems and make calculations more efficient.

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