SOLUTION: if n^2+m^2 = 11nm, show that 1/2(logn +logm) =log(n-m/3).

Algebra.Com
Question 1097315: if n^2+m^2 = 11nm, show that
1/2(logn +logm) =log(n-m/3).

Answer by ikleyn(52803)   (Show Source): You can put this solution on YOUR website!
.
 = 11nm   is equivalent to  

 = 9nm   is equivalent to  

 = 9nm   is equivalent to  

 = nm   is equivalent to  

 = nm.



Under the assumption  n > 0,  m > 0,  n > m  it implies that


2*log((n-m)/3) = log(n) + log(m),    which is equivalent to


(1/2)*(log(n) + log(m)) = log((n-m)/3).

QED.


------------------------
On logarithms and their properties, see the lessons
    - WHAT IS the logarithm
    - Properties of the logarithm
    - Change of Base Formula for logarithms
    - Solving logarithmic equations
    - Using logarithms to solve real world problems
in this site.

Also,  you have this free of charge online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this online textbook under the topic "Logarithms".


Save the link to this online textbook together with its description

Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson

to your archive and use it when it is needed.



RELATED QUESTIONS

What is the value of the given expression: log sq.rt.(m^3/n) a. 1/2 log m - log n (answered by Jk22)
m/(m-n)(m+n)/n+1/(m+n)^2 (answered by mangopeeler07)
show that log(1×2×3) = log 1 + log 2 + log 3. Is it true for any three positive numbers (answered by greenestamps)
I am asked to express in terms of log m and log n... (answered by Theo)
Log(subscript 2)M^6... (answered by fractalier)
LogM+LogY=(2/3)LogX Solve for... (answered by stanbon,palanisamy)
if log 3=m and log 2=n, find log (600) in terms of m and... (answered by Alan3354,lwsshak3,richard1234)
Please help me with my homework, thankyou in advance for your time! :) For positive... (answered by jim_thompson5910)
if M and N are two matrices such that MN=N and NM=M show that M^2 + N^2= M +... (answered by richard1234)