Solve the equations by finding the exact solution.
a 3= x -3 what is x
b In e = In like a check mark 7 with a 6 under the 7 -3 In e x is what
Thank you very much for your time
3 = x-3
6 = x
As for the other, I can't quite decode your weird text. I can say that
ln e = 1
ln √n = 1/2 ln n
ln a - ln b = ln(a/b)
If you have
ln e = ln √6 - 3ln x
1 = ln√6 - ln x^3
1 = ln √(6/x^6)
e = √(6/x^6)
6/x^6 = e^2
x^6 = 6/e^2
x = (6/e^2)^(1/6)
I suspect that is not what you were after, but it should show you how to manipulate logs a little.
thank you Steve it does give me a direction in which to guide me.
a) To solve the equation "3 = x - 3" for x, you want to isolate the variable x on one side of the equation.
One way to do this is by adding 3 to both sides of the equation:
3 + 3 = x - 3 + 3
Simplifying the equation gives you:
6 = x
Therefore, the exact solution for x is x = 6.
b) The equation you provided, "In e = In √(7)^6 - 3In e x," seems to involve natural logarithms (ln).
Assuming the equation is: ln(1) = ln(√(7)^6) - 3ln(e) * x
First, simplify the equation by evaluating the logarithmic expressions:
0 = ln(7^3) - 3 * 1 * x
Next, simplify further:
0 = 3ln(7) - 3x
To isolate the variable, subtract 3ln(7) from both sides:
-3ln(7) = -3x
Then, divide both sides by -3 to solve for x:
x = ln(7)
Therefore, the exact solution for x is x = ln(7).