Simplify a Log Expression?

Question

-a log[(a+sqrt(a^2-y^2))/y]

I could not simplify it. I have double-checked the placement of parentheses.

Answer 1

You are right, there is little to simplify here, except maybe the division inside the log, which becomes subtraction:

-a{log (a + sqrt(a^2-y^2)) - log y}

When I get a formula like this, I sometimes define b = a/y, so that a = b*y, and the expression becomes

- b y log [b + sqrt(b^2 - 1)]

That's as simple as you'll get it.

Answer 2

The log of a quotient is equal to the difference of the logs

Log (a/b) = Log (a) - Log (b)

You can also shift the coefficient to the exponent of the Log if it helps

a * Log (b) = Log [(b)^a]

Answer 3

-a log[(a+sqrt(a^2 - y^2))/y]

=a log[y/(a + sqrt(a^2 - y^2))]
or
log[y/(a + sqrt(a^2 - y^2))]^a
which are all equivalent expressions and not simplifications.
There is no simpler way of writing the expression.

Answer 4

simplify the rooted eqn.
remember PEMDAS.
and remember log of a number is simply the expotential reciprocal.

just wanted to give some reminders.

Answer 5

I looks like all you can do it move the "/y" outside the log term as
-log(y)

Answer 6

-a * log((a + sqrt(a^2 - y^2))/y)

-a * log(a + sqrt(a^2 - y^2)) - log(y)

as far as i can get

-alog(a + sqrt(a^2 - y^2)) + alog(y)
or
alog(y) - alog(a + sqrt(a^2 - y^2))

Answer 7

Quish! Whew!

Answer 8

98/989765

Answer 9

you are correct,
it cannot be simplified