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.

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

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

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

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, 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.

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?