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

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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...

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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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