How do you condense #Ln x + 2Ln y#?

2 Answers
Jim G.
Jun 1, 2016

#ln(xy^2)#

Explanation:

Using the #color(blue)"laws of logarithms"#

#•logx+logy=log(xy).............(1)#

#•logx^nhArrnlogx................(2)#

Although expressed in terms of log ,these laws apply to logs of any base.

using (2) : #2lny=lny^2#

using (1) : #lnx+lny^2=ln(xy^2)#

#rArrlnx+2lny=ln(xy^2)#

Tony B
Jun 1, 2016

#ln(xy^2)#

Explanation:

#color(blue)("Introduction to some principles of logs")#

Multiplication of source numbers results in addition of logs.

So #log(ab)=log(a)+log(b)#

The product of a constant and a log is the consequence of the source value raised to the power of that constant.

#2log(a) = log(a^2)#

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Answering your question")#

Consider: #2ln(y)#

Another way of writing this is: #ln(y^2)#

Consider: #ln(x)+ln(y^2)#

Another way of writing this is: #ln(xy^2)#

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