Before solving the equation, we'll have to impose
constraints of existence of
logarithms.
2x>0
x>0
Now,
we could apply the power property of logarithms:
2log 5 =
log 5^2 = log 25
We'll re-write the
equation:
log 2x + log 25 =
2
Now, we'll apply the product property of
logarithms:
log 2x + log 25 = log 2*25*x = log
50x
log 50x = 2 => 50x = 10^2 => 50x =
100
We'll divide by 50 both
sides:
x = 2
>0
Because the solution is in the interval (0,
+inf.), the solution is admissible.
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