SOLUTION: How can I write the expression 2.1n x-1n y+3. 1n z as a single lograithm. The periods after the 2 and 3 stands for the (times) sign not periods.

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Question 113499: How can I write the expression 2.1n x-1n y+3. 1n z as a single lograithm. The periods after the 2 and 3 stands for the (times) sign not periods.

Answer by solver91311(12126) About Me  (Show Source):
You can put this solution on YOUR website!
2%2Aln%28x%29-ln%28y%29%2B3%2Aln%28z%29

First rule to apply is that a%2Aln%28x%29=ln%28x%5Ea%29, so we can write:

ln%28x%5E2%29%2Bln%28y%5E%28-1%29%29%2Bln%28z%5E3%29
ln%28x%5E2%29%2Bln%281%2Fy%29%2Bln%28z%5E3%29

The next rule is that the log of the product is the sum of the logs of the factors, like this:

ln%28abc%29=ln%28a%29%2Bln%28b%29%2Bln%28c%29. So for this problem:

ln%28x%5E2%29%2Bln%281%2Fy%29%2Bln%28z%5E3%29=ln%28x%5E2z%5E3%2Fy%29

Hope this helps,
John

P.S. Next time use the asterisk '*' (Shift-8) to make the multiplication sign as in 2 * 3 = 6