Solve Logarithmic Equation: 9_{x} + 3_{x} = \frac{4}{3}

[the_storm]

Homework Statement

9$$_{x}$$ + 3$$_{x}$$ = $$\frac{4}{3}$$

Homework Equations

Solve the equation

The Attempt at a Solution

3$$_{2x}$$ + 3$$_{x}$$ = $$\frac{4}{3}$$
I try to take ln for both sides ...? but how and there is a plus sign between them?

 

[micromass]

Put $$3^x=y$$ and solve for y.

 

[Mark44]

Homework Statement

9$$_{x}$$ + 3$$_{x}$$ = $$\frac{4}{3}$$

Homework Equations

Solve the equation

The Attempt at a Solution

3$$_{2x}$$ + 3$$_{x}$$ = $$\frac{4}{3}$$
I try to take ln for both sides ...? but how and there is a plus sign between them?

Taking the log of both sides won't do you any good since there's no way to simplify the log of a sum. You have a good start, though - just rewrite the equation as
$$3^{2x} + 3^{x} - \frac{4}{3} = 0$$
This is quadratic in form. You can use micromass's suggestion or factor the equation as-is.

 

[the_storm]

thank you guys done :) :)