Question

solve for k: ln(k+1)-ln(k)=.125

Answer 1

Properties of logs: ln(x)-ln(y)=ln(x/y)
so: ln(k+1)-ln(k)=ln((k+1)/k)=ln(1+1/k)
Remember e^ln(x)=x.
So if you make all terms e^(something) it makes it much easier:
=> e^ln(1+1/k)=e^0.125
=> 1+1/k=e^0.125
=> 1/k=e^0.125-1
=> k=1/(e^0.125-1)
=> k= 7.51041...

Answer 2

thanks so much