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 x^{2}^{ }= 2 lin x, ln x^{4} = 4 ln x, etc.

Thus, 3 ln x - 4 ln x^{4 }= 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