sum and/or difference of logs, help appreciated.

[ochocki]

I don't even know where to begin with this one. either way you guys have been such a great help, I have one more question:

Write as the sum and/or difference of logs. Do not use exponents.


I will try to write this as well as I can as I don't understand TeX.

log (7rootm * 8rootn / r²)
base5

for the 7rootm the 7 is the index, and the m is the radicand. Same goes for the other.

please ask if you need clarification.

 

[pka]

Why don't you go to "FORUM HELP" and download TeXAide.
I doubt anyone of us can make heads or tails of you post.

 

[galactus]

When I started on the forums, I didn't know LaTex either, but it's easy to learn.
Start with something easy, like \(\displaystyle \frac{1}{2x+3}\)

Click on 'quote' at the upper right hand corner of this post to see the code I used to display that.

 

[stapel]

I don't understand TeX.

log (7rootm * 8rootn / r²)
base5

for the 7rootm the 7 is the index, and the m is the radicand. Same goes for the other.

Does the above means the following?

. . . . .log_5 ( 7th-rt[m] 8th-rt[n] / r^2 )

...where "kth-rt[]" means "the k-th root of []" and "log_b ()" means "the log, base b, of ()".

Thank you.

Eliz.

 

[soroban]

Hello, ochocki!

Write as the sum and/or difference of logs: \(\displaystyle \L\:\log_5\left(\frac{\sqrt[7]{m}\cdot\sqrt[8]{n}}{r^2}\right)\)

We have: \(\displaystyle \L\log_5\left(\frac{m^{\frac{1}{7}}\cdot n^{\frac{1}{8}}}{r^2}\right)\)

. . . . \(\displaystyle \L=\;\log_5\left(m^{\frac{1}{7}}\right)\,+\,\log_5\left(n^{\frac{1}{8}}\right)\,-\,\log_5(r^2)\)

. . . . \(\displaystyle \L=\;\frac{1}{7}\cdot\log_5(m)\,+\,\frac{1}{8}\cdot\log_5(n)\,-\,2\cdot\log_5(r)\)