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).