# Math help, how do you get the answer?

The problem is: .5^x = 8^(2-x) The answer is: x=3 But how do you get that answer? I've been trying to figure it out for hours.... Someone please help....

ok i guess i cant do what i doe on facebook where i hit shift and enter at the same time so try to bare with me as i show my work.... : x log(.5)= (2-x)log(8) distribute: x log(.5)= 2log(8)- x log(8) get both x's on the same side: xlog(.5)+xlog(8)=2log(8) factor out the x: x(log[.5]+log[8])=2log8 divide both sides by (log[.5]+log[8]): x= 2log8/(log[.5]+log[8]) simply: x=3..... yeah its a lot of steps.... thanks for showing me the other way of doing it i think it might be easier...

Ok first you change your bases so they are the same and we can solve for the exponents. What's a base that can be used for both 0.5 and 8? Answer is 2.

So you get

2^(-1)(x)= 2(3)(2-x)

We didn't actually change the equation in any way because 2^(-1) is the equivalent of 0.5 and 2^3 is the equivalent of 8.

Now we can solve for the exponents. -1(x) = 3(2-x) -1x= 6 -3x 2x=6 x=3 Viola.

ok that seems easier then how my teacher explained it... he had me do it this way...