anonymous
  • anonymous
Solve for x: 3^x - 2 = 8/3^x
Mathematics
katieb
  • katieb
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

Get this expert

answer on brainly

SEE EXPERT ANSWER

Get your free account and access expert answers to this
and thousands of other questions

anonymous
  • anonymous
\[3^{x} - 2 = 8/3^{x}\]
anonymous
  • anonymous
multiply both sides by 3 to the x to eliminate the denominator and subtract eight from both sides\[3^{2x}-2*3^{x}-8=0\]
anonymous
  • anonymous
Do you follow so far?

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

anonymous
  • anonymous
Yes, I got \[3^{x} = 4 , 3^{x} = -2\]
anonymous
  • anonymous
Then what?
anonymous
  • 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
anonymous
  • anonymous
Thank you soo much!! That was very helpful! :D

Looking for something else?

Not the answer you are looking for? Search for more explanations.