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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