Question

1000(0.98) to the power of N = 250
(0.98)to the power of N = 1/4
0.98)= 1/4 to the power of 1/N
please help me solve WITHOUT using LOG

Answer 1

using Log the answer is 68.6 how do i get this with out using log?

Answer 2

I know there are approximations to the ln, if that is what you mean:

\[ ln(1±x) \approx ±x -\frac{x^2}{2} ±\frac{x^3}{3} \]
you can use that, and (knowing?) ln(2)= 0.693 (some people memorize this!)

N ln(1-0.02)= ln(2^-2)
N ( -0.02 - 0.0004/2 ) = -2*0.693 (ignore x^3 term)
N= -2*0.693/-0.0202 = 68.6

Answer 3

thankyou!