Please help me understand the problem 2 + 4 * 3^x =4, solve for x ?

Question

psymon · Answer

$$2+4(3^{x})= 4$$
Is that correct?

anonymous · Answer

yes

anonymous · Answer

I see 4(3^x) = 2, but I don't know how to bring down x, log perhaps???

psymon · Answer

Get the exponential part by itself as much as possible first. So now you would divide by 4 to get 3^x by itself.

anonymous · Answer

ok! thats an idea 3^x = 2/3

psymon · Answer

Should be (1/2) on the otherside xD

anonymous · Answer

ugh you are right Psymom, so can I do x log 3 = log 1/2 ???

anonymous · Answer

*Psymon

psymon · Answer

Well, it would have to be calculator work. So yeah, you'd divide both sides by ln3

anonymous · Answer

x = (log1/2)log 3 ??? I'm running the calc now

anonymous · Answer

If a take log on one side, don't I also apply that to the other side?

psymon · Answer

Well, you started with this before the ln:
$$3^{x} = \frac{ 1 }{ 2 }$$ Then we took the natural log of both sides to help get the x out of the exponent position:
$$xln(3) = \ln(\frac{ 1 }{ 2 })$$ Now I would divide both sides by ln(3) to get:
$$x = \frac{ \ln(\frac{ 1 }{ 2 }) }{ \ln(3) }\approx -.691$$

isaiah.feynman · Answer

I hate myself

anonymous · Answer

you both have been helpful! We're all here to learn and help. Thank you both and thanks Psymon, I was getting the idea but my computation was wrong. Thanks for the correction!

psymon · Answer

Yep, np ^_^

anonymous · Answer

:-)

isaiah.feynman · Answer

Giving an erroneous calculation is not helpful!