Solve for x if log (x^2) - log 2x = 2.
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log (x^2) - log 2x = 2
We will use the logarithm properties to solve for x.
First, we know that log a - log b = log (a/b)
==> log x^2 - log 2x = log (x^2/2x) = log (x/2)
Now we will substitute into the equation.
==> log (x/2) = 2
Now we will use the exponent form to rewrite the equation.
==> (x/2) = 10^2
==> x/2 = 100
Now we will multiply by 2.
==> x = 200
Then the answer for the equation is x= 200
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The equation log (x^2) - log 2x = 2 has to be solved for x.
log (x^2) - log 2x = 2
Use the property of logarithm, log a - log b = log(a/b)
log(x^2/(2x)) = 2
log(x/2) = 2
If log_b x = y, x = b^y
x/2 = 10^2
x/2 = 100
x = 200
The solution of the given equation is x = 200
To solve for x if log (x^2) - log 2x = 2.
Solution:
By property of logarithms, log(a^m) = m * log a ,
log a = log b = log (a/b).
So log x^2 - log2x = 2 = log 10^2, as log10^2 = 2log 10 = 2.
log (x^2 )/(2x) = log 10^2.
We take anti logarithms:
x^2/(2x) = 100.
x^2 = 200x.
x^2-200x = 0.
x(x-200) = 0.
x = 0, or x= 200.
For x= 0, log(x) is undefined. So x= 200 is a valid solution.
x = 200.
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