## anonymous 3 years ago Solve for x: 3^x - 2 = 8/3^x

1. anonymous

$3^{x} - 2 = 8/3^{x}$

2. anonymous

multiply both sides by 3 to the x to eliminate the denominator and subtract eight from both sides$3^{2x}-2*3^{x}-8=0$

3. anonymous

4. anonymous

Yes, I got $3^{x} = 4 , 3^{x} = -2$

5. anonymous

Then what?

6. anonymous

Now treat it as a quadratic equation set equal to zero and use the quadratic formula to solve for 3 to the x, because 3 to the x was squared, just like a variable, and we have second and third terms as well.$\frac{ 2 +\sqrt{4-4*(-8)} }{ 2 }$ You can ignore the possibility where you subtract the square root, since that would give a negative answer, which 3 to the x can't equal. Solve and you get $\frac{ 8 }{ 2 }=4=3^{x}$Now you should take the natural logarithm of both sides and solve.$\ln 4=\ln 3^{x}$Pull the exponent down and divide both sides by the natural log of 3$\ln 4=x \ln 3$$\frac{ \ln4 }{ \ln3 }=x$ That should be your answer

7. anonymous

Thank you soo much!! That was very helpful! :D