Solve for X: 4*(5^x)-3(0.4^2x)=11 | Quick Algebra Homework

[TheExibo]

Homework Statement

4*(5^x)-3(0.4^2x)=11

In case it doesn't make sense, in the attempted solution it's written out better

Homework Equations

The Attempt at a Solution

http://imgur.com/SnpFQZV

Thanks!

 

[Mark44]

Homework Statement

5*(4^x)-3(0.4^2x)=11

In case it doesn't make sense, in the attempted solution it's written out better

Homework Equations

The Attempt at a Solution

http://imgur.com/SnpFQZV

Thanks!

In the image, which is difficult to read, you have a different problem:
##4 \cdot 5^x - 3 \cdot 0.4^{2x} = 11##
Is what you have in the image the equation you need to solve? Also, are you sure you have written the problem correctly? Both problems seem more difficult than the usual kinds of problems of this type.

 

[TheExibo]

Yes! I'm really bad with typing out equations, but that's exactly it!

 

[Ray Vickson]

Yes! I'm really bad with typing out equations, but that's exactly it!

It would have been 100% clear if you had put parentheses around the '2x', like this:
4 * 5^x -3 * (0.4)^(2x).

 

[Mark44]

If there's a way to solve this equation analytically, I don't see it. What I would do is try either a graphical approach, by graphing y = 4 * 5^2 - 3 * .4^(2x) and seeing where the graph crosses the line y = 11, or try an iterative approach, starting with an educated guess.

If x = 1, the left side is 4 * 5^1 - 3 * .4^2 = 20 - .48 = 19.52
If x = 2, the left side is slightly less than 100, so we're getting farther away from a solution, so try numbers smaller than 1.