Skip to main content
Search IntMath
Close

450+ Math Lessons written by Math Professors and Teachers

5 Million+ Students Helped Each Year

1200+ Articles Written by Math Educators and Enthusiasts

Simplifying and Teaching Math for Over 23 Years

Tips, tricks, lessons, and tutoring to help reduce test anxiety and move to the top of the class.

IntMath forum | Exponential & Logarithmic Functions

Log Laws [Solved!]

My question

I refer to 3. Logarithm Laws

For this email I will use a convention where if a^x = b then x is written as log(a) b. i.e. the base of the log is written in parantheses. So if for example we have (ab)^c = d then c is given by log(ab) d.

Now I think that log(xy) z can be rewritten as following

log(xy) z = 1/[(1/log(x) z) + (1/log(y) z)]

Have you heard of such an identity?

Relevant page

3. Logarithm Laws

What I've done so far

I've been thinking about this for some time now.

X

I refer to <a href="/exponential-logarithmic-functions/3-logarithm-laws.php">3. Logarithm Laws</a>

For this email I will use a convention where if a^x = b then x is written as log(a) b. i.e. the base of the log is written in parantheses. So if for example we have (ab)^c = d then c is given by log(ab) d.

Now I think that log(xy) z can be rewritten as following

log(xy) z = 1/[(1/log(x) z) + (1/log(y) z)]

Have you heard of such an identity?
Relevant page

<a href="/exponential-logarithmic-functions/3-logarithm-laws.php">3. Logarithm Laws</a>

What I've done so far

I've been thinking about this for some time now.

Re: Log Laws

Hi Michael

It is quite hard to read your question. You are encouraged to use the math entry system.

Actually, I have not seen this before, but it is true. I am using change of base formula (which is on this page: 5. Natural Logarithms (base e)

I am changing to base 10, so I just write "log" (but I could change it to any base).

`\text{LHS}`

`= \log{xy} z`

`= \frac {log z}{\log xy}`

`= \frac {log z}{\log x + \log y}`

`\text{RHS}`

`= \frac{1}{(\log x / \log z)} + \frac{\log y}{\log z}`

`= \frac{1}{(\log x + \log y)/\log z}`

`= \frac{\log z}{\log x + \log y}`

Phew!

I'm not sure what you would use it for, though!

Regards

X

Hi Michael

It is quite hard to read your question. You are encouraged to use the math entry system.

Actually, I have not seen this before, but it is true. I am using change of base formula (which is on this page: <a href="/exponential-logarithmic-functions/5-logs-base-e-ln.php">5. Natural Logarithms <span class="noWrap">(base e)</span></a>

I am changing to base 10, so I just write "log" (but I could change it to any base).

`\text{LHS}`

`= \log{xy} z`

`= \frac {log z}{\log xy}`

`= \frac {log z}{\log x + \log y}`

`\text{RHS}`

`= \frac{1}{(\log x / \log z)} + \frac{\log y}{\log z}`

`= \frac{1}{(\log x + \log y)/\log z}`

`= \frac{\log z}{\log x + \log y}`

Phew!

I'm not sure what you would use it for, though!

Regards

Re: Log Laws

Thanks. I doubt it has a use, too, but I found it interesting.

X

Thanks. I doubt it has a use, too, but I found it interesting.

Reply

You need to be logged in to reply.

Related Exponential & Logarithmic Functions questions

Exponential & Logarithmic Functions lessons on IntMath

top

Tips, tricks, lessons, and tutoring to help reduce test anxiety and move to the top of the class.