Solve the following equation for the exact value of x. If there is no solution, enter DNE. If there is just one solution, enter DNE for x2. If there are 2 solutions, enter the greater solution for x1.
ln(7x2+4)=ln(16x+17).
x1=
x2=
check my answer please:
x1=2.92141422
x2=-0.63569994
thank you
although, if they want exact values, maybe you should put
(8+√155)/7
and
(8-√155)/7
Looks good to me
To solve the equation ln(7x^2 + 4) = ln(16x + 17), we can start by applying the property of logarithms that states ln(a) = ln(b) if and only if a = b.
So, we can set the expressions inside the logarithms equal to each other:
7x^2 + 4 = 16x + 17
Next, we rearrange the equation to isolate the quadratic term:
7x^2 - 16x + 13 = 0
To solve this quadratic equation, we can use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
In this case, a = 7, b = -16, and c = 13.
Plugging in these values, we can calculate the discriminant (b^2 - 4ac) to determine the number of solutions:
Discriminant = (-16)^2 - 4(7)(13)
= 256 - 364
= -108
Since the discriminant is negative (-108 < 0), the equation has no real solutions. Therefore, both x1 and x2 do not exist (DNE).
Thus, the provided values of x1 = 2.92141422 and x2 = -0.63569994 are incorrect.