SOLUTION: hello tutors: (2logx)=x over 25. im not sure how to go about this log equation.do i cross multiply.change 25 to 5^2..really not sure...Can i have a step by step explanation. Thank

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: hello tutors: (2logx)=x over 25. im not sure how to go about this log equation.do i cross multiply.change 25 to 5^2..really not sure...Can i have a step by step explanation. Thank      Log On


   

Question 1152654: hello tutors: (2logx)=x over 25. im not sure how to go about this log equation.do i cross multiply.change 25 to 5^2..really not sure...Can i have a step by step explanation. Thank you tutors for all your great help.
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
2log%28x%29=x%2F25
2%2A25log%28x%29=x
log%28x%29=x%2F50....................if f+%28x+%29=g+%28x+%29, then a%5E%28f+%28x+%29%29=a%5E%28g%28x%29%29
10%5E%28log%2810%2Cx%29%29=10%5E%28x%2F50%29.......simplify : 10%5E%28log%2810%2Cx%29%29=+x
x=10%5E%28x%2F50%29...............use Lambert form: xe%5E%28-+ln+%2810+%29x%2F50%29%29=1

rewrite the equation with :+u=-%28ln+%2810+%29x%29%2F50 and x=+-50u%2Fln+%2810%29

%28-+50u%2Fln+%2810%29%29e%5Eu=1=> in Lambert form is e%5Eu%2Au=-%28ln%2810%29%2F50%29

solve e%5Eu%2Au=-ln%2810%29%2F50%29

u=-2ln%2810%29, u=+W%5B0%5D%28-ln%2810%29%2F50%29

substitute back :u=-%28ln%2810%29x%29%2F50%29, solve for x
-%28ln+%2810+%29x%29%2F50=-2%2Aln%2810%29
-%28ln+%2810+%29%29x=-2%2A50%2Aln%2810%29
-ln+%2810+%29x=-100%2Aln%2810%29
x=%28-100%2Aln%2810%29%29%2F%28-ln+%2810%29%29
x=100

solve -%28ln+%2810+%29%29x%2F50=+W%5B0%5D%28-ln%2810%29%2F50%29
-%28ln+%2810+%29%29x=50W%5B0%5D%28%28-ln%2810%29%29%2F50%29%29

x=50W%5B0%5D%28%28-ln%2810%29%29%2F50%29%2F%28-%28ln+%2810+%29%29%29%29

x=-%2850W%5B0%5D%28-ln%2810%29%2F50%29%29%2Fln+%2810%29

x=-%2850W%5B0%5D%28-1%2F50%29%29

x=50W%5B0%5D%2F50

The solutions are:

x=100, x=50W%5B0%5D%2F50