Question

since f(x)=lnx at x=[1,8] satisfies the mean value theorem. How would you find c that concludes the theorem

Answer 1

you solve the equation f'(c)=f(8)-f(1)/7

Answer 2

since it satisfies the mean value thm then we conclude the above result to be true

Answer 3

the rest is easy i suppose

Answer 4

so you would just set f'(c)=1/x=.3? i found the .3 in the equation you typed out

Answer 5

f'(c)=1/c
the left hand side is equal to ln(8)/7
so we got 1/c=ln(8)/7
then c=7/ln(8)

Answer 6

looks like you got the right thing
but you don't need to write it in decimal
keep it 7/ln(8) or 7/3ln(2)
unless you are asked to approximate the value in decimal places