# What Does The Logarithm of the Power of a Number Mean?

• Euler
In summary, the rule for logarithms states that the logarithm of the power of a number is equal to that power multiplied by the logarithm of the number. This can also be expressed as x = log_a(y), where y = a^x. The definition of logarithm may vary, but it is commonly defined as the power to which a base must be raised to yield a given number.
Euler
I'm reading a book and there is a section about rules to do with logarithms but one of them I don't understand, it is very wordy and I just can't get what it means.

It says "The logarithm of the power of a number is that power multiplied by the logarithm." I really don't understand what that means, can anyone who does break it down for me?

$$\log (x^a) = a\log x$$

The logarithm "log" of the power "a" of a number "x" on the LHS, the power "a" multiplied by the logarithm [of that number] "log a" on the RHS.

If $y= a^x$ then $x= log_a(y)$. That is often used as the definition of the logarithm. Exactly how was "$log_a(x)$" defined in your class?

1 person
HallsofIvy said:
If $y= a^x$ then $x= log_a(y)$. That is often used as the definition of the logarithm. Exactly how was "$log_a(x)$" defined in your class?

How can x = the log of x? If we do 2^3 = 8 for example then log to the base 2 of 8 = 3, yes? I am still quite confused. I don't know why I can't understand this.

Euler said:
How can x = the log of x?

Who said ##x=\log(x)##?
Euler said:
If we do 2^3 = 8 for example then log to the base 2 of 8 = 3, yes? I am still quite confused. I don't know why I can't understand this.
yes. It is correct.
As HallsofIvy said before, if ##y=a^x## then ##\log_a(y)=x##.
I understand it this way: To what power should x be raised to get y?

Who said ##x=\log(x)##?

yes. It is correct.
As HallsofIvy said before, if ##y=a^x## then ##\log_a(y)=x##.
I understand it this way: To what power should x be raised to get y?

I'm sorry, I misread HallsofIvy's post. I think I understand now.

## Related to What Does The Logarithm of the Power of a Number Mean?

The phrase "Please help explain what this means?" is a request for clarification or further explanation. It suggests that the speaker does not fully understand the meaning of something and is seeking assistance.

## 2. Why is it important to ask for clarification?

Asking for clarification is important because it allows for better understanding and prevents misunderstandings. It also shows that the speaker is actively trying to learn and engage in the conversation.

## 3. How do I effectively ask for clarification?

To effectively ask for clarification, be specific about what you do not understand and try to provide context or examples to help the person explaining. It is also important to listen actively and ask follow-up questions if needed.

## 4. What should I do if I am still confused after asking for clarification?

If you are still confused after asking for clarification, don't be afraid to ask for additional help or resources. You can also try to break down the information into smaller parts and ask for clarification on each part individually.

## 5. How can I improve my own explanations when someone asks for help?

To improve your explanations, try to use simple and clear language, provide examples or visuals, and actively listen to the person's questions and concerns. You can also ask for feedback to see if your explanation was effective.

• General Math
Replies
8
Views
1K
• General Math
Replies
15
Views
3K
• General Math
Replies
6
Views
2K
• General Math
Replies
9
Views
845
• General Math
Replies
3
Views
1K
• General Math
Replies
14
Views
2K
• General Math
Replies
3
Views
698
• General Math
Replies
5
Views
1K
• General Math
Replies
4
Views
7K
• General Math
Replies
20
Views
2K