Question 760852
{{{c*5.4^k=5.8*c*1.92^k}}} is the direct translation of the description.


Notice you can divide left and right sides by c.
{{{5.4^k=(5.8)1.92^k}}}


Logarithms of both sides will be equal.
{{{log((5.4^k))=log((5.8*1.92^k))}}}


As an approach, using base of 10 and ...
{{{k*log(10,5.4)=log(10,5.8)+k*log(10,1.92)}}}
{{{k(log(10,5.4)-log(10,1.92))=log(10,5.8)}}}
{{{highlight(k=(log(10,5.8))/(log(10,5.4)-log(10,1.92)))}}}


Finish by either table of logarithms or scientific calculator.


{{{k=0.7634/(0.7324-0.2833)}}}
{{{highlight(k=1.70)}}}