Question 4694
1.{{{ln7 + ln(x-3) = ln(x + 15)}}}
{{{ln(7(x-3) = ln(x+15))}}}. Now just raise everything to the power e, to remove the natural logs:


7(x-3) = x+15
7x-21 = x+15
6x = 36
x = 6


2. {{{28 = 19 + 12^(x-7)}}}


{{{9 = 12^(x-7)}}}. Take logs to the base 10:


{{{log9 = log12^(x-7)}}}
{{{log9 = (x-7)log12}}}
{{{x-7 = (log9)/(log12)}}}
x-7 = 0.884228
so x = 7.884228


3. {{{e^(3x-4) = 1/e^(x-12)}}}


{{{e^(3x-4) = e^(-(x-12))}}}
{{{e^(3x-4) = e^(12-x)}}}. Now take natural logs of both sides, to remove the "e":


3x-4 = 12-x
4x = 16
x = 4


--> check these answers in the original questions.


jon.