Question 267905
Assume the problem is:
{{{e^(-x)}}}={{{(e^4)^(x+3)}}}
:
Use the nat logs
{{{ln(e^(-x))}}}={{{ln((e^4)^(x+3))}}}
:
use the log equiv of exponents
{{{-x*ln(e)}}} = {{{(x+3)*ln(e^4)}}}
:
we know the ln of e = 1, and ln(e^4) = 4, therefore it is greatly simplified
{{{-x*1}}} = {{{(x+3)*(4)}}}
-x = 4(x+3)
-x = 4x + 12
-12 = 4x + x
-12 = 5x
x = {{{-12/5}}}
:
:
Check this on your calc
enter e^(-(-12/5)) = 11.023
enter (e^4)^((-12/5)+3)= 11.023, equality reigns