SOLUTION: write 3log u - log v - 4log z expression as a single logarithm
Algebra.Com
Question 206233: write 3log u - log v - 4log z expression as a single logarithm
Found 2 solutions by stanbon, Theo:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
write 3log u - log v - 4log z expression as a single logarithm
---
log u^3 -log v - log z^4
----
= log[u^3/(vz^4)]
=================
Cheers,
Stan H.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
your problem is stated as
-----
There are 3 basic rules of logarithms.
you will be using rules 2 and 3 as shown below.
rule number 1 does not apply to this problem
-----
rule number 1 states that
-----
rule number 2 states that
-----
rule number 3 states that
-----
your equation of can be first converted to using rule number 3 in reverse.
-----
your equation of can be first converted to and then converted to using rule number 2 in reverse if we apply the rule successively as we scan from left to right which we can do as long as there are no parentheses telling us to do otherwise. Anything within parentheses is always done first. That is not the case here since we have no parentheses in your original problem statement.
-----
your final form is
-----
to prove that this is true, we'll untangle it using the rules 1 and 2 of logarithms and we should be able to get back to the original equation.
-----
your answer of becomes using rule number 2
-----
this becomes using rule number 3.
-----
this becomes using rule number 2.
-----
this becomes using rule number 3.
-----
your original problem stated as
is equivalent to my final version of your original problem as because my parentheses, in this case, do not alter the order of the operations to be performed.
-----
RELATED QUESTIONS
Write each expression as a single logarithm
3log(5)^(u) +... (answered by jim_thompson5910)
write the expression as a single logarithm
2log u-3log v- 2log... (answered by dabanfield)
Write the expression as a single logarithm... (answered by jim_thompson5910)
Write the logarithmic expression
3log x – 2log y + log z
as a single... (answered by ikleyn)
Write each expression as a single logarithm.
a) 2log (base2) x - 4log (base2) y + 3log... (answered by venugopalramana)
Write the expression as a single logarithm:... (answered by lynnlo,KMST)
Rewrite the expression
5logx-3log(x^2-1)+4log(x-1)
as a single logarithm... (answered by lwsshak3)
Condense each expression to a single logarithm
log6/3
4log(3)-4log(8)
log(2)+... (answered by lynnlo)
Using properties of logarithms write 4log(xy)-3log(yz) as a single... (answered by user_dude2008)