I can't find my scientific calculator...
Can anyone solve this for me?

If ln X = 6 and ln y = 2, then ln (x squared/y) = ?
Could you write the steps if you have a way of solving without the sci. calculator.

"ln" is symbol for natural logrithms
Thanks

well, it's been about 14 years since i did this type of mathematics, but this is what i can remember. No scientific calculator needed.



ln (x squared / y) = ln (x multiplied by x/y).

ln (x multiplied by x/y) = ln x + ln (x/y)

ln (x/y) = ln x - ln y

therefore ln (x squared / y) = ln x - lny + ln x.

therefore your answer is 2ln x -ln y

which would be 10.

I believe.

i hope that helps - and any corrections gratefully received - i'm very rusty!

Oh man...it's been waaaay too long...

I think you're gonna need a calculator because the natural log ln has "e" as its base, and e = 2.71828 which doesn't come out clean.

Still:

if ln (y) = 2 then y = e^2
if ln (x) = 6 then x= e^6

( e^2 means "e squared" and e^6 means "e to the 6th power")

So your question becomes ln ( e^12 / e^2 )
= ln ( e ^ 10 )
= 10

So I agree with TheFrog, though I totally don't understand how he got 10.

Sorry I was stupid and missed the "ln" edit.
[This message was edited Fri Jun 25 13:53:21 2004 by Spookymuffin]

hi teller.

i think maybe i should explain my algebraic method a bit more clearly.

the essential thing to remember is the following two universal equations which deal with products and inverse products:

ln (ab) = ln (a) + ln (b)

and ln (a/b) = ln (a) - ln (b).

using those equations in the above formulation, you can quite easily separate xsquared/y into x multiplied by x/y (which is equivalent to ab in the above equation).

you therefore have an equation which reads ln (x) + ln (x/y).

now, using the second of the ab equations, we can break down the ln(x/y) into ln (x) - ln (y).

putting the two together, you get ln (x) + ln (x) - ln (y).

which = 2x6 - 2 = 10.


accidentally used an = instead of a + edit.
[This message was edited Fri Jun 25 14:01:41 2004 by TheFrog]

Frog can do it he's the Man
If He can't solve it
NO ONE CAN!!!!


Goooo, FRoggie!!!!!

TheFrog said:

Gotcha... I didn't remember any of those other algebraic rules.

Well...there's definitely more than one to way to skin a cat.

madartista said:

well that's very sweet chris.

teller's is a perfect way of solving the problem. just depends who was your teacher at school, i guess.

TheFrog said:

oh, I didn't mean that as a slight to Teller at all.

just leading a cheer for TheFrog as prescribed in the Stalker Guide Book.

Hats off 2 all you maths geeks.

I've got severe maths phobia and run away crying at the simplest problems.

T H A N K Y O U B O T H!
What a great site!

TheFrog

teller

madartista said:

and you are a much loved stalker.

teller said:

skinning a cat...

seriously, thanks - i hadn't even thought of just using e and eliminating it through cancellation with the ln. very bright.

teller said:

I've often thought that if I get another cat, I will name him Skin.

madartista said:

You do that.

Cats emit a very different form of "natural log."

Yep... TEN!

Wait, don't go.....one more

If 8 to the "x" power = 15 and 8 to the "y" power = 25, then 8 to the (2x+y) power =?

steps???

SensualMelody said:

You're not cheating on something, are u?

SensualMelody said:

okay, this one's simpler...

i'm going to use teller's notation because it's much clearer.

8^x = 15.
8^y = 25.

(8^x) multiplied by (8^x) = 8^2x = 15 multiplied by 15 = 175.

(8^2x) + (8^y) = 8^(2x+y).

so, 175 + 25 = 8^(2x +y).

so the answer's 200.

i used to totally understand all of this. i loved statistics..although this looks very much like pure maths which i hated as i just could'nt see the point .who cares about infinity

wow...it really is amazing how soon we forget or get totally rusty.

just don't tell my father...hes a maths teacher!

Frog is wrong!

He didn't phrase it in the form of a question!

The correct answer is "What is 10?"

SensualMelody said:

This begs to use 8 as the log base. So when I say "log" I mean log base 8 instead of "e." So:

If 8^x = 15 then x = log(15)
And if 8^y = 25 then y = log(25)

The question is: 8^(2x + y) = ?

Log both sides: 2x + y = log (?)

Substituting, we get: 2 log(15) + log(25) = logz

Using TheFrog's algebra:

log(15) + log(15) + log(25) = logz
log ( 5625) = log (?)
5625 = ?

I didn't get 200...I must have screwed something up!

TheFrog said:

Wait a minute...that looks wrong...

Maybe I didn't screw mine up! :O

Gotta run...good luck Melody!

teller said:

I thought this looked fishy.

teller said:

no, i bet i did!

i thought you could do it without logs, because a^b multiplied by a^c = a^(b+c)



so i was thinking a = 8, and so...

8^x multiplied by 8^x = 8^(x + x) = 8^2x. and then 8^2x multiplied by 8^y = 8^(2x + y)

2the9s said:

Dammit!!! I think 9s is right!

teller said:

sorry, that is wrong. i meant, 8^2x multiplied by 8^y = 8^2x+y.

so the answer would be 175 multiplied by 25, which = 4375.

but that's still a different answer to teller.

oh okay!


i made a mistake of thinking 15x15 was 175, when it's 225.

so you can do it with logs, or without logs, and it still ends up with 225 x 25 = 5625.

skinning cat different ways again.

except this time i don't know my 15 times table.