Simplify-exact form
2ln xpower squareroot e
and Expand the log
ln 3power sqaure root x^2y/x+5
You are not getting a reply because probably none of us can really decipher what you mean.
is it
2ln x√e ?
if so, then it would be 2√e(ln x)
the second one is even more difficult to figure out. Can you put brackets around the critical parts of the expression?
U=3j
To simplify the given expression 2ln(x√e), we can follow these steps:
Step 1: Apply the properties of logarithms.
The natural logarithm of a product is equal to the sum of the natural logarithms of each factor:
ln(ab) = ln(a) + ln(b)
Step 2: Simplify the expression inside the logarithm.
The square root of e can be written as e^(1/2):
ln(x√e) = ln(x * e^(1/2))
Step 3: Apply the property of logarithms.
The natural logarithm of an exponential expression can be written as a product of the exponent and the logarithm of the base:
ln(a^b) = b * ln(a)
Applying this property:
ln(x * e^(1/2)) = ln(x) + ln(e^(1/2))
Step 4: Simplify further.
Since ln(e) equals 1, we have:
ln(x) + ln(e^(1/2)) = ln(x) + (1/2)
Therefore, the simplified form of 2ln(x√e) is 2ln(x) + 1.