Posted by **Alicia** on Tuesday, July 28, 2009 at 12:20am.

Please express in terms of sums and differences in logarithms.

log a x^3 y^2 z

- Algebra -
**drwls**, Tuesday, July 28, 2009 at 1:14am
Add the logs of every term in the product. For the x^3 term, you get 3logx. You do the rest. Let us know if you want your answer checked

- Algebra -
**Alicia**, Tuesday, July 28, 2009 at 1:26am
1 log a 3log x 2log y 1 logz Is this correct?

- Algebra -
**drwls**, Tuesday, July 28, 2009 at 7:21am
No. You have to add the logs of each term. Remember that

log (abc) = log a + log b + log c etc.

Your answer should be

log (a x^3 y^2 z) = log a + 3 log x + 2 log y + log z

- Algebra -
**mathland**, Tuesday, July 28, 2009 at 11:33am
Please express in terms of sums and differences in logarithms.

log a x^3 y^2 z

For log_a (x^3) we can use the rule

log_b (m^n) = nlog_b (x).

The log_a (x^3) becomes 3xlog_a (x).

===================================

We usethe same rule for y^2.

y^2 becomes 2log_y.

And finally, z becomes log_z.

We now use the sum rule:

log_b(mn) = log_b(m) + log_b(n).

3log_a(x) + 2log_y + log_z

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