precalculus help!!?

Question

help with problem any help is appreciated with some sort of explanation!!!

Find the inverse function f of f(x) = 8x-4/2x+6. Then prove that the inverse function is the inverse of f algebraically.

For how many integers between 1 and 20 can the natural logarithms be approximated given that ln 2= .6931, ln 3= 1.0986, ln 5= 1.6094? Approximate these logarithms without using a calculator. (please show the work!!!!!)

Answer 1

The function (8x^2+6x-4/2)/x has no inverse because for each value of f you get two values of x
2) log4 = log 2^2 = 2log2
log6 = log(2*3) = log2+log3
log7 (not possible)
log8 =log(2^3) = 3 log 2
log 9 = log 3^2 =3log3
10=2*5
11( not possible)
12=4*3
13(not possible)
14(not possible
15=3*5
16=2^4
17(not possible
18=2*9
19(not possible)
20= 4*5 so log 20 = 2log 2 +log5 Just to remember

Answer 2

write y instead of f(x)
then find the value of x
y=(8x-4)/(2x+6)

2xy+6y=8x-4
6y+4=8x-2xy
6y+4=x(8-2y)

x=(6y+4)/(8-2y)

The answer is
f^-1 (x)=(6x+4)/(8-2x)


except 1 and 20
the logarithms of 2,3,4,5,6,8,9,10,12,15,16,18
can be calculated using ln2,ln3,ln5

That is 12 numbers.

if we include 1 and 20
it will be 14 numbers