What is the solution to the equation 3 ^(1 – 2x) = 2 ?

Question

anonymous · Answer

I got -0.6309300955 as my answer but I don't think it's right...

anonymous · Answer

take log base three of both sides?

anonymous · Answer

I know it's like (1-2x)log3=log2

anonymous · Answer

I'm getting something closer to .2 on my calculator, but you should try solving with logarithms to get an exact value.

anonymous · Answer

Alright,thanks for the help!

anonymous · Answer

yeah, just change that above equation to $$1-2x = \log_{3} 2$$ and you should get it.

anonymous · Answer

@sarahcoop3r - Your method is right so far.  
(1-2x)log(3)=log(2)

Divide both sides by log(3) to get rid of it on the left side:
$$1-2x=\frac{\log(3)}{\log(2)}$$
Subtract 1 from both sides$$-2x=\frac{\log(3)}{\log(2)}-1$$
And finally, divide by -2 to get x by itself:
$$x=-\frac{1}{2}(\frac{\log(3)}{\log(2)}-1)$$
You should be able to plug that into your calculator to get a final answer.