-3^(-x)-6=-3^x+10Solve the equation below for x by graphing plz

Accepted Solution

to graph it, just graph [tex]y=-3^{-x}-6[/tex] and [tex]y=-3^x+10[/tex] and see where they intersect

I would like to solve it by using math and not graphing
if you don't want to see the math, just don't scroll down
the graphical meathod is above, first line, just read it

multiply both sides by -1
multiply both sides by [tex]3^x[/tex]
minus 1 from both sides and minus 6(3^x) from both sides
use u subsitution
we can rewrite it as
now factor
I mean use quadratic formula
for [tex]ax^2+bx+c=0[/tex] [tex]x=\frac{-b+/-\sqrt{b^2-4ac}}{2a}[/tex]
so for 0=u^2-16u-1, a=1, b=-16, c=-1
remember that u=3^x so u>0
if we have u=8+√65, it's fine, but u=8-√65 is negative and not allowed
so therfor
if you take the log base 3 of both sides you get
if you use ln then