## having trouble writing a logarithmic expression as a single

Complex numbers, rational functions, logarithms, sequences and series, matrix operations, etc.
milynx
Posts: 7
Joined: Mon Jul 27, 2009 9:46 pm
Contact:

### having trouble writing a logarithmic expression as a single

Question: Write the logarithmic expression 3 log _2 X + log 2_2 Y - 5 log_2 Z as a single logarithm. Assume X anY are positive numbers. Thank YOU!!

stapel_eliz
Posts: 1628
Joined: Mon Dec 08, 2008 4:22 pm
Contact:
Write the logarithmic expression 3 log _2 X + log 2_2 Y - 5 log_2 Z as a single logarithm.
Apply the multiplier-to-power log rule to move the multipliers 3 and 5 inside their respective logs. Then use the addition rule to combine the first two logs into one. Lastly, apply the subtraction log rule to combine this new log with the third log in the original expression.

You should end up with $\log_2\left(\frac{x^2 y}{z^5}\right)$, assuming the first "2" in the second term is a typo.

milynx
Posts: 7
Joined: Mon Jul 27, 2009 9:46 pm
Contact:

### Re: having trouble writing a logarithmic expression as a single

thank you. yes it was a typo.