View Full Version : Approximation of ln8 using the power rule

06-13-2011, 03:16 PM
I have been stuck on this for hours on end. I really need help quickly on this.

The source of the problem is this:

The approximation of the natural logarithm of 2: ln 2 ? 0.693. Based on this approximation and the power rule for logarithmic expressions, how could you approximate ln 8, without a calculator?

At first I tried to switch from ln 8 to loge8. I have been stuck ever since. I had asked my instructor where I'm going wrong, and their response was "This problem doesn't involve you using e. you have to figure out how to break down 8 to have a base of 2 with an exponent. If you can do that then you will already know what ln of 2 is because its given in the problem. you will then need to take what ln of two is and multiply it by the exponent that came down in the front due to the power rule of logs."

If I can't change the natural log to something else, how do I even do this, let alone do it using the power rule? I did cheat and use my calculator to find the ln of 8 is 2.079. Still I have no idea how to get to that or explain it.

Please help!

06-13-2011, 04:51 PM
Remember that ln(8)=ln(2^{3})=3ln(2)