Solve for x and give answers as exact solutions
First, this problem involves natural logarithms, which have base e. The exact solution will be in terms of e .
We can begin by taking advantage of the logarithmic property of exponents, i.e., ln x2 = 2 lin x, ln x4 = 4 ln x, etc.
Thus, 3 ln x - 4 ln x4 = 2 can be rewritten as:
3 ln x - 4(4) ln x = 2 , or
3 ln x - 16 ln x = 2, which is
-13 ln x = 2, or
ln x = -2/13
The base is e, so we convert the ln function into an exponential function:
x = e -2/13
This is the exact solution. The decimal solution to 4 places, is x = 0.8574