simplify (ln(8x^2))/(ln(4x))

Thanks!

To simplify the expression (ln(8x^2))/(ln(4x)), you can use the properties of logarithms and some basic algebraic manipulations.

First, let's use the logarithmic property that states ln(a) - ln(b) = ln(a/b). Applying this property, we can rewrite the expression as ln(8x^2) - ln(4x):

(ln(8x^2) - ln(4x)) / ln(4x)

Next, another logarithmic property states that ln(a) + ln(b) = ln(ab). We can use this property to combine the two logarithms into one:

ln((8x^2) / (4x))

Now, let's simplify the numerator:

8x^2 / 4x

Simplifying further:

2x

Therefore, the simplified expression is 2x.