Question

Substitution of the log ex: (ln |x|)^2/x

Answer 1

To simplify the expression (ln|x|)^2/x, you can use the property of logarithms and rewrite it as 2ln(x)/x.

Step-by-step explanation:

The given expression is (ln|x|)^2/x. Let's work step by step:

1. The natural logarithm ln is the inverse of the exponential function e. So, ln(e^x) = x.
2. Using this property, we can rewrite the expression as ln(x)^2/x.
3. Next, write the exponent as multiplication: ln(x * x)/x.
4. Using the logarithm property log(xy) = log(x) + log(y), we can rewrite the expression as (ln(x) + ln(x))/x.
5. Since both logarithms have the same base (ln), we can simplify further to 2ln(x)/x.

So, the given expression simplifies to 2ln(x)/x.