What is the solution for log x^3 - log10x = log 40?

Given the logarithm equation log x^3 - log 10x = log
40.

We need to find x values that satisfies the
equation.

We will use logarithm properties to
solve.

First, we know that log a - log b = log
a/b.

==> log x^3 - log 10x = log
40

==> log x^3/10x = log
40

Now we will
simplify.

==> log x^2/10 = log
40

Now, we know that of the logarithms are equal, then the
bases are equal too.

Or, if log a = log b ==> a =
b

==>  x^2/10 = 40

We
will multiply by 10.

==> x^2 =
40*10

==> x^2 = 400

Now
we will take the root of both sides.

==> x1=
20

==> x2= -20 ( we will not consider this answer
because log 10x is not defined.

Then, the
answer is : x = 20