Equation: 4^x + 7^x = 11^x

[Math Tutor]

Solve the equation:
[tex]4^x + 7^x = 11^x[/tex]

[Guest]

Divide both side by [tex]8^x[/tex]

[tex]\left(\frac{4}{8}\right)^x+\left(\frac{7}{8}\right)^x = \left(\frac{11}{8}\right)^x[/tex]

Now L.H.S is a Combination of strictly decreasing function While R.H.S is strictly In increasing function.

So Thses two curve Intersect at exactly one point . so one real value of [tex]x[/tex]

Which is [tex]x = 1[/tex]

[Guest]

I think it will be more simple to divide both side by [tex]11^x[/tex]. Then in right we have a constant=1. Left is strictly decreasing.