x^-2-x^-3/2x simply logarithm

Answer 1

To simplify the expression x^(-2) - x^(-3)/2x using logarithms, we can rewrite it as follows:

x^(-2) - x^(-3)/(2x) = 1/x^2 - 1/(2x^4)

Now, let's take the logarithm of both sides of the equation:

log(1/x^2 - 1/(2x^4))

Using the property log(a/b) = log(a) - log(b), we can split the logarithm:

log(1/x^2) - log(1/(2x^4))

Again, using the property log(1/x) = -log(x), we can simplify further:

-2log(x) - (-log(2x^4))

Simplifying the expressions inside the logarithms:
-2log(x) + log(2) + 4log(x)

Combining like terms:
2log(x) + log(2) + 4log(x)

Therefore, the simplified expression using logarithms is 2log(x) + log(2) + 4log(x).