e^(1+2lnx)
-----------
x^2
simplify
maybe take ln of top and bottom
(1+2 lnx)
---------
2 lnx
1 + 1/(2 lnx)
1 + 1/lnx^2
e^(1+2lnx) = e^1 * e^2lnx
= e * (e^lnx)^2
= e * x^2
That should help some
Tsk Tsk, Damon
ok so ex^2
----- = e
x^2
Thank you
To simplify the expression (e^(1+2lnx))/x^2, we can start by using the properties of logarithms and exponentials.
Step 1: Recall that ln(x) is the natural logarithm of x, which is the logarithm to the base e. Also, note that the exponential function e^x is the inverse of the natural logarithm.
Step 2: We can rewrite 2ln(x) as ln(x^2) using the property that ln(a^b) = b * ln(a).
So, e^(1+2lnx) = e^1 * e^(2lnx) = e * e^(ln(x^2)).
Step 3: Using the property that e^(ln(a)) = a, we can simplify e^(ln(x^2)) as x^2.
So, e^(1+2lnx) = e * e^(ln(x^2)) = ex^2.
Step 4: Combining this result with the denominator x^2, we get the simplified expression:
ex^2 / x^2.
Finally, we can simplify further:
ex^2 / x^2 = e * (x^2 / x^2) = e.