Please condense the expression.
1/2ln(x^2+1)-4ln1/2-1/2[ln(x-4)+lnx]
To condense the given expression, we can use properties of logarithms to simplify it. Here's how you can do it step by step:
Step 1: Start by using the rule that states ln(a) - ln(b) = ln(a/b):
1/2ln(x^2+1) - 4ln(1/2) - 1/2[ln(x-4) + ln(x)]
= 1/2ln(x^2+1) - 4ln(1/2) - 1/2ln(x-4) - 1/2ln(x)
Step 2: Next, simplify ln(1/2) using the rule ln(1/a) = -ln(a):
= 1/2ln(x^2+1) - 4(-ln(2)) - 1/2ln(x-4) - 1/2ln(x)
= 1/2ln(x^2+1) + 4ln(2) - 1/2ln(x-4) - 1/2ln(x)
Step 3: Combine like terms:
= 1/2ln(x^2+1) - 1/2ln(x-4) - 1/2ln(x) + 4ln(2)
And that's the condensed form of the given expression!