solve:
2 ln e= ln sqrt of 7/x-2 ln e
what would be x?
Assuming parentheses as shown below, and recalling that ln(e) = 1,
2 ln e= ln sqrt(7/(x-2)) ln e
2 = ln √(7/(x-2))
√7/(x-2)) = e^2
7/(x-2) = e^4
x-2 = 7e^-4
x = 2 + 7e^-4
Thanks Steve I have it now, But the answer checked out to be e^-4+ln sqrt 7
To solve the equation, we need to rearrange it and isolate the variable x.
Given:
2 ln e = ln(sqrt(7/x)) - 2 ln e
First, let's simplify the equation by using the properties of logarithms:
2 ln e = ln(sqrt(7/x)) - 2 ln e
Since ln e equals 1, the equation can be simplified further:
2 = ln(sqrt(7/x)) - 2
Next, let's eliminate the natural logarithm by converting it to exponent form:
e^2 = sqrt(7/x) / e^2
Now, we can eliminate the square root by squaring both sides of the equation:
e^(2*2) = (sqrt(7/x) / e^2)^2
Simplifying:
e^4 = (7/x) / e^4
Rearranging the equation:
(x/7) = e^4 / e^4
Simplifying further:
x/7 = 1
To solve for x, multiply both sides of the equation by 7:
x = 7
So, the solution to the equation is x = 7.