SOLUTION: Show that log base a (a^2 - x^2) = 2 + log base a (1 - x^2/a^2)

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Question 1113133: Show that log base a (a^2 - x^2) = 2 + log base a (1 - x^2/a^2)
Answer by MathTherapy(10801) About Me  (Show Source):
You can put this solution on YOUR website!
Show that log base a (a^2 - x^2) = 2 + log base a (1 - x^2/a^2)
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log+%28a%2C+%28a%5E2+-+x%5E2%29%29+=+2+%2B+log+%28a%2C+%281+-+x%5E2%2Fa%5E2%29%29
Let's focus on the R.H.S
 ---- Converting 2 to log+%28a%2C+%28a%5E2%29%29
log+%28a%2C+%28a%5E2+-+x%5E2%29%29+=+log+%28a%2C+a%5E2%281+-+x%5E2%2Fa%5E2%29%29 --- Applying log+%28b%2C+%28c%29%29+%2B+log+%28b%2C+%28%28d%29%29%29 = log+%28b%2C+%28c%2Ad%29%29
log+%28a%2C+%28a%5E2+-+x%5E2%29%29+=+log+%28a%2C+%28a%5E2+-+x%5E2%29%29 ---- Distributing on R.H.S.
              L.H.S. = R.H.S.