Need help solving logarithms

Calculus
Tutor: None Selected Time limit: 1 Day

Solve for x: 

2 log(base 5) x = log(base 5) (x^2 - 6x + 2)

Jun 10th, 2015

Thank you for the opportunity to help you with your question!

since they have the same base you can write it like this

2 log(5) x = log(5) (x^2-6x+2) the answer is 1/3

since you can write it as

2log(x)=log(x^2-6x+2)

all over 

log(5)


2log(x)- log((x-6)(x+2)) all divided by log(5) = 0

2log(x)-log((x-6)(x+2))=0 now simple solving 

and you get x =1/3


Please let me know if you need any clarification. I'm always happy to answer your questions.
Jun 10th, 2015

how did you find the x-6 and x+2 because when i foiled that out in turned into x^2 - 4x - 12 not x^2 - 6x +2 like it should be

Jun 10th, 2015

Here i will write down all the steps i did give me a minute

Jun 10th, 2015

log(5)x^2=log(5)(x^2-6x+2) using log rules

now since the base is the same you can remove it and solve for the inside 

the way i did before was a way i do in my head and i did not use quadratic rule its a bit different but a quicker way to solve but anyhow since the base is the same we remove it and solve for the inside similar to an exponential function you solve for the power

x^2=x^2-6x+2

0=-6x+2

6x=2

x=2/6 x=1/3

Jun 10th, 2015

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