SOLUTION: I need step by step explanations for problems like {{{log(b)(x^2-15)=log(b)(6x+1)}}}

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Question 398624: I need step by step explanations for problems like log%28b%29%28x%5E2-15%29=log%28b%29%286x%2B1%29
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
log%28b%2Cx%5E2+-15%29+=+log%28b%2C6x+%2B+1%29
Suppose I say
c+=+x%5E2+-+15 and
d+=+6x+%2B+1
Then I can rewrite equation as:
log%28b%2Cc%29+=+log%28b%2Cd%29
The main thing to keep in mind is "logs are exponents"
This equation says:
The log to the base b which gives me c is equal to
the log to the base b which gives me d
--------------------------------------------
This is 2 logs equal to each other, so I can say that log = e
b%5Ee+=+c is true
b%5Ee+=+d is true
So, c+=+d must be true
and, since I said
c+=+x%5E2+-+15 and
d+=+6x+%2B+1
It follows
x%5E2+-+15+=+6x+%2B+1
x%5E2+-+6x+-+16+=+0
By looking at it, I see
%28x+-+8%29%2A%28x+%2B+2%29
The solutions are:
x+=+8 and
x+=+-2