Solve for x:

3^x - 2 = 8/3^x

Question

Solve for x:

3^x - 2 = 8/3^x

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

Do you follow so far?

anonymous · Answer

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

anonymous · Answer

Then what?

anonymous · Answer

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

anonymous · Answer

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