Yes (a) is the correct result.SteveDC said:Homework Statement
Got to part of a problem where I have exp(-3ln(x)) and I am confused as to whether the next step is:
a) exp(ln(x^-3)) = x^-3
or
b) exp(-ln(x^3)) = -x^3
I think the correct step is (a) but not certain, any help would be great :)
Here it appears you're saying ##e^{-a} = -e^a##, that you can simply pull the minus sign out front, which you probably know isn't correct.SteveDC said:b) exp(-ln(x^3)) = -x^3
Exp(-3ln(x)) is a mathematical expression that represents the exponential function with a base of e raised to the power of -3 times the natural logarithm of x.
Solving Exp(-3ln(x)) can be useful in simplifying complex mathematical equations and in finding the inverse of exponential functions.
To solve Exp(-3ln(x)), you can use the property of logarithms that states ln(a^b) = b*ln(a). This means that you can rewrite the expression as x^-3, which can then be simplified to 1/x^3.
The only restriction when solving Exp(-3ln(x)) is that x must be a positive number. This is because the natural logarithm of a negative number is undefined.
Solving Exp(-3ln(x)) can be used in various fields such as physics, chemistry, and economics to model exponential growth and decay phenomena.