log x+6(2x^2-7x+16)=2

Question

solve for all values of x

Answer 1

As written, there is no parenthesis around x+6. Do we take the log of the entire left side? If so, taking 10 to a power on both sides, we get

12 x^2 - 41 x - 4 = 0. The quadratic formula yields the solution (41 +- √1873)/24 or -.09492,3.51159

Answer 2

The values in this equation are very hard to graph for small x which is where the root lies.

There appears to be a root between 0 and 1.

There are 2 ways to get at an approximate root:

1) use Newton's Method starting with x=1

2) use a computer to compute successive values of the equation (you can use a spreadsheet).