Here is what I did, but I'm not sure that this is valid:

(ab)^x = e^{x ln(ab)} = e^{x ln(a) + x ln(b)} = e^{x ln(a)}e^{x ln(b)} = a^xb^x

What do you think?

Thanks!

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- April 17th 2011, 10:24 PMjoatmonProve the 4th Law of Exponents
Here is what I did, but I'm not sure that this is valid:

(ab)^x = e^{x ln(ab)} = e^{x ln(a) + x ln(b)} = e^{x ln(a)}e^{x ln(b)} = a^xb^x

What do you think?

Thanks! - April 17th 2011, 10:40 PMProve It
I assume you would not be able to use logarithm laws until you have proven all of the index laws...

I would say...

http://quicklatex.com/cache3/ql_624c...91bc415_l3.png - April 17th 2011, 10:48 PMjoatmon
That's a good idea. They show us how they prove the first two laws of exponents, and they use logarithms to do it. My attempt is a variation on what the book did for the first two proofs.

I'll try your way, too.

Thanks! - April 18th 2011, 07:25 AMDrSteve
Prove It's argument only works if x is a positive integer. A more formal proof (for x a positive integer) would require mathematical induction.

For x an arbitrary real number, the OP's method can be used. - April 18th 2011, 03:54 PMProve It