- #1

lillybeans

- 68

- 1

## Homework Statement

Find limit of x --> 3 of

ln(1+2x)-ln7

-----------

x-3

## Homework Equations

The properties of log?

## The Attempt at a Solution

= ln ((1+2x)/7)^(1/x-3)

then make h=x-3; x=h+3

limit as h --> 0

= ln ((1 + 2h + 6)/7) ^ (1/x-3)

= ln ((7 + 2h)/7) ^ (1/x-3)

= ln (1 + 2/7h)^(1/x-3)

then I did it the non-algebraic way and plugged in 0.01 and got 0.2587 as the answer, which is coincidentally 2/7 (this number is found in the equation also)! But how do I prove/arrive at that? I do remember that (1+h)^(1/h) = e. But what do I do now?

Help is appreciated and many thanks.