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.

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

Quote:

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Originally Posted by galactus

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

Quote:

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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

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

See, . The same as if

Oh well, I tried.

Quote:

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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, . The same as if

Oh well, I tried.

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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?