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January 28th, 2012, 12:58 AM  #1 
Newbie Joined: Jan 2012 Posts: 3 Thanks: 0  Hard logarithm question
Hello! Attached is a very hard logarithm question that I couldn't answer in my math test. If someone could help me answer it, I would very much appreciate it Thanks in advance 
January 28th, 2012, 01:13 AM  #2 
Senior Member Joined: Jul 2011 Posts: 227 Thanks: 0  Re: Hard logarithm question
You are given: Your first step to make a common denominator for the RHS is a good start: Now use some logarithm rules: To continue make the substitution which will give you a quadratic equation in 
January 28th, 2012, 01:20 AM  #3 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs  Re: Hard logarithm question
We are given to solve: Multiply through by as we know for all real x: Arrange as quadratic on : Factor: Assuming x is real, we must discard the negative root, and are left with: Convert from exponential to logarithmic form: 
January 28th, 2012, 02:23 AM  #4 
Newbie Joined: Jan 2012 Posts: 3 Thanks: 0  Re: Hard logarithm question
Thank you! I'm really impressed with this forum, the answers are clear and succinct 
January 22nd, 2017, 01:45 AM  #5 
Newbie Joined: Jan 2017 From: Somewhere Posts: 1 Thanks: 0  Answer
x = log[base 5](3)  1
Last edited by Wizzy0630; January 22nd, 2017 at 01:47 AM. 
May 31st, 2017, 02:37 AM  #6 
Newbie Joined: May 2017 From: China Posts: 1 Thanks: 0  Answer
Hey, I know I may be too late to answer you now. You do not need to use logarithm for this question. Set 5^x as y, and rewrite the equation as 2*5*y = 1+3/y. Then continue the equation and factorize the quadratic you get. Keep going until you get your answer. Thanks 

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