SOLUTION: 4. (25 pts) Write the logarithmic expression as a single logarithm and, if possible, simplify. Show some work. log 2 + log (x2 � 4) � log (5x � 10) 3. (25 pts) Write the g

Question 34875: 4. (25 pts) Write the logarithmic expression as a single logarithm and, if possible, simplify.
Show some work.
log 2 + log (x2 � 4) � log (5x � 10)
3. (25 pts) Write the given logarithm in terms of sums and/or differences of log x, log y, and log z. Show some work.
log(x2/y sqrt z)
I have spent the last 6 hours trying to figure these out and I have no idea of how to find the answer. I think getting started is the hardest part I am unsure of where to start. I have tried removing () by mutiplying by 2 then combining, but I still seem to have to many numbers to follow the quotient rule. If at all possible can you provide a descriptive explanation of this for me.
Thank you so much
Minta Mattocks

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Write the logarithmic expression as a single logarithm and, if possible, simplify.Show some work.
log 2 + log (x^2 � 4) � log (5x � 10)
=log[2(x^2-4)/(5x-10)]
Explanation:
When you add logs you get the log of the product: log2 + log(x^2-4)=
log (2(x^2-4)
When you subtract logs you get the log of the quotient.
log A - log B = log(A/B)
3. (25 pts) Write the given logarithm in terms of sums and/or differences of log x, log y, and log z. Show some work.
log(x^2/y sqrt z)
= logx^2-log(ysqrtz)
= 2logx -[logy +logsqrtz]
= 2logx -logy -(1/2)logz
Explanation: Same as for the 1st problem with this additional rule:
log A^n = nlog A. That's why logx^2 becomes 2logx and log sqrtz becomes
(1/2)log z
Cheers,
Stan H.

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