4 In e= In (�ã(3))/(x)-4 In e Solve the equations by finding the exact solution.
On my screen your intended symbol did not show up correctly.
did you mean:
ln e = ln (√3/(x) ) - 4ln e ?
if so, then
5ln e = ln (√3/x)
ln e^5 = ln (√3/x)
anti-ln it
e^5 = √3/x
x = √3/e^5
Let me know if your equation was meant differently.
Thank you for answering my question.But I really do not know what happend to the 4 in front of the equation?
ahh, my error, I thought it was question #4
easy to fix
4 ln e = ln (√3/(x) ) - 4ln e
8ln e = ln (√3/x)
ln e^8 = ln (√3/x)
anti-ln it
e^8 = √3/x
x = √3/e^8
Thank you for your help.
To solve the equation, we need to simplify the expression and isolate the variable x.
Given:
4 * ln(�ã(3))/(x) - 4 * ln(e) = 0
First, let's simplify the expression:
4 * ln(�ã(3))/(x) - 4 * ln(e) = 0
ln(�ã(3))/(x) - ln(e^4) = 0
ln(�ã(3))/(x) - ln(e^4) = ln(1) (because ln(e) = 1)
Using the property of logarithms that ln(a) - ln(b) = ln(a/b), we can simplify further:
ln(�ã(3))/(x * e^4) = ln(1)
Now, since the natural logarithm function is a one-to-one function, the only way for ln(�ã(3))/(x * e^4) to equal ln(1) is if the arguments are equal:
�ã(3))/(x * e^4) = 1
To solve for x, we can cross-multiply and solve the resulting equation:
�ã(3) = x * e^4
Now, square both sides of the equation to get rid of the square root:
(�ã(3))^2 = (x * e^4)^2
3 = x^2 * e^8
Finally, solve for x:
x^2 = 3 / e^8
x = ±�ã(3 / e^8)
So the exact solutions for x are ±�ã(3 / e^8).