Writing a Logarithm as a Single Term w/o a log

incognito · #1 May 6, 2007, 05:35 PM

Hello,
I need help solving this problem:

"Write 10^(log3x^2+log5x) as a single term that does not contain a logarithm"

Now, I tried to get rid of the log's by changing everything to a common log, but that just leaves trying a 0 to as X.
This doesn't seem right.

Can someone please explain how to solve this problem.
Many thanks.

ebaines · May 7, 2007, 06:18 AM

Where exactly are you getting stumped? If you apply the various identities for powers and logarithms, you'll get it:

10^(log A) = A
log(a*b) = log(a) + log(b)
log(a^b) = b log(a)
10^(a+b) = 10^a * 10^b
10^(a*b) = (10^a)^b

incognito · May 7, 2007, 08:59 AM

Quote:

Originally Posted by galactus

$10^{log(3x^{2})+log(5x)}=10^{log(3x^{2}\cdot{5x})} =3x^{2}\cdot{5x}=15x^{3}$

Isn't that still leaving a log term? 10^log15x^3

incognito · May 7, 2007, 09:05 AM

Quote:

Originally Posted by ebaines

Where exactly are you getting stumped? If you apply the various identities for powers and logarithms, you'll get it:

10^(log A) = A
log(a*b) = log(a) + log(b)
log(a^b) = b log(a)
10^(a+b) = 10^a * 10^b
10^(a*b) = (10^a)^b

I ended up getting 150x^3
I multiplied the exponential logs, then used the 3rd property of logarithms to move the exponent in from of log 10, then I canceled out logs and multiplied everything together.
Is that even possible??

incognito · May 7, 2007, 01:43 PM

Quote:

Originally Posted by galactus

Incognito, I gave you a worked out solution. 15x^3. I see no log in that. They have been eliminated

See, $10^{log(a)}=a$ . The same as if $e^{ln(a)}=a$

Oh well, I tried.

NNNOOOO WWWWAAAAAIIIITTTTT!!
Haha, my teacher only had one lecture on logarithms and the book is of no help.
I didn't know that when you "added" logs, the log part cancels out.
Is this a Theorem or Property?



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