# Solve for x if log (x^2) - log 2x = 2.

hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted on

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

tonys538 | Student, Undergraduate | (Level 1) Valedictorian

Posted on

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

neela | High School Teacher | (Level 3) Valedictorian

Posted on

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 ab  and

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.