Question 959160
Please explain how to solve:

{{{ e^(x)-8e^(-x)=7 }}}


and


solve for x (exact answer)
{{{ 10^(10-x)=16^(x) }}}


Thank you
<pre>{{{e^x - 8e^(- x) = 7}}}
{{{e^x - 8e^(- x) - 7 = 0}}}
{{{e^x - 8(1/e^x) - 7 = 0}}}
{{{e^x - (8/e^x) - 7 = 0}}}
{{{e^x * e^x - 8 - 7e^x = 0}}} --------- Multiplying by LCD, {{{e^x}}}
{{{e^(2x) - 7e^x - 8 = 0}}}
{{{(e^x - 8)(e^x + 1) = 0}}}
{{{e^x - 8 = 0}}}		OR		{{{e^x = - 1}}} (ignore)
{{{e^x = 8}}} ----- Exponential form
ln 8 = x --- Logarithmic form
{{{highlight_green(x = 2.079442)}}}

{{{10^(10 - x) = 16^x}}} ----------- Exponential form
{{{log 10^(10 - x) = log 16^x}}} ----- Taking log of both sides
10 - x (log 10) = x (log 16)
(10 – x) * 1 = x log 16
10 – x = x log 16
10 = (x log 16) + x
10 = x[(log 16) + 1)]
{{{highlight_green(x = 10/((log 16) + 1))}}}