Saturday, September 3, 2011

If log 5a - log (2a-3) = 1, find a.

Given the logarithm
equation:


log 5a - log (2a-3) =
1


We need to find the value of "a" that satisfies the
equation.


We will use the logarithm properties to
solve.


We know that log a - log b = log
(a/b)


==> log 5a - log (2a-3) = log (5a/(2a-3) =
1


Also, we know that log 10 =
1


==> log 5a/(2a-3) = log
10


Now that we have the logs are equal. then the bases are
equal too.


==> 5a/(2a-3) =
10


We will multiply by 2a-3 both
sides.


==> 5a =
10(2a-3)


==> 5a = 20a -
30


==> -15a = -30


We
will divide by -15


==> a =
2

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