Question 569464
Assume the problem is:
{{{123=500e^(-0.12x)}}}
rewrite it
{{{500e^(-0.12x)}}} = 123
divide both sides by 500
{{{e^(-0.12x)}}} = {{{123/500}}}
{{{e^(-0.12x)}}} = .246
:
Using nat logs
{{{ln(e^(-0.12x))}}} = ln(.246)
:
the log equiv of exponents
-.12x*ln(e) = ln(.246)
;
find {{{e^x}}} of both sides, the nat log of e is 1
-.12x = -1.4024
;
x = {{{(-1.4024)/(-.12)}}}
x = +11.6869
:
:
We can check this on a good calc: enter 500*e^(-.12*11.6869). results 122.999 ~ 123