log 2x - log 5 = 1

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To solve log2x - log5 = 1

Solution:

We know that 1 = log10. Therefore,

log2x -log5 = log 10

lo2x = log10 +log5

log2x = log(10*5), as loga +logb = log(ab).

log2x = log50. Take antilogarithms

2x = 50

2x/2 = 50/2

x =25.

We'll add log 5 both sides:

log 2x - log 5 + log 5 = 1 + log 5

log 2x = log 10 + log 5

We'll use the product property, for the sum from the right side:

log 2x = log 50

We'll subtract log 50 both sides:

log 2x - log 50 = 0

We'll use the quotient property of the logarithms:

log 2x/50 = 0

2x/50 = 10^0

We'll cross multiply:

2x = 1*50

We'll divide by 2:

x = 25

Since x is positive, the equation has the solution x=25.

log 2x - log 5 = 1

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

==>log 2x - log 5 = 1

==> log (2x/5) = 1

Now we know that log10 = 1

==> log (2x/5) = log 10

==> 2x/5 = 10

==> 2x = 50

==> x= 25

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