Question 476213
a. {{{ 5/(3-e^(-x)) = 7 }}} multiply both sides by {{{(3-e^(-x))}}}
{{{ 5= 7*(3-e^(-x))  }}}divide by 7
{{{3-e^(-x) =5/7}}} subtract 3
{{{-e^(-x) =5/7-3}}} divide by -1
{{{e^(-x) =-5/7+3}}}
{{{e^(-x) =16/7}}} logarithm
{{{-x=ln(16/7)}}} divide by -1
{{{x=-ln(16/7)}}}
If use the scintific calculator {{{x=-0.8267}}}
.
b. Rewrite the answer so that each individual logarithm from part a is written as a sum or difference of logarithms of prime numbers
{{{x=-ln(16/7)}}}
Use formula {{{ln(a/b)=lna-lnb}}}
{{{x=-(ln16-ln7)}}}
{{{x=ln7-ln16}}}