use the law of logarithms to expand and simplify.

ln(e^x)/(1+e^x)

Please help, i have no idea..

To expand and simplify the expression ln(e^x)/(1+e^x) using the law of logarithms, we need to apply the properties of logarithms and algebraic simplifications. Here's how you can do it step by step:

Step 1: Apply the property ln(a^b) = b ln(a) to expand the numerator:
ln(e^x) = x ln(e) = x

Step 2: Rewrite the denominator as a single logarithm:
1 + e^x = e^0 + e^x = e^0 * e^x + e^x = e^0 * e^x + e^x * e^0 = (e^0 + e^x) * e^0
= (1 + e^x) * 1

Step 3: Rewrite the expression with the new expanded numerator and denominator:
x / [(1 + e^x) * ln(e^x)]

Step 4: Simplify the expression:
x / [(1 + e^x) * ln(e^x)] = x / [ln(e^x) + ln(1)]
(ln(1) = 0, so ln(e^x) + ln(1) = ln(e^x) + 0 = ln(e^x))

x / ln(e^x) = x / x = 1

Therefore, the expanded and simplified expression is equal to 1.