Can anyone help me with the following question?
3-3^x=5^x. Find the value x.
Thank you.

Question

Can anyone help me with the following question?
3-3^x=5^x. Find the value x.
Thank you.

turingtest · Answer

$$3-3^x=5^x$$and you want to solve for x ?

anonymous · Answer

Yes.

turingtest · Answer

I'm sorry, I know of no analytic way to do this http://www.wolframalpha.com/input/?i=solve%203-3%5Ex%3D5%5Ex&t=crmtb01

asnaseer · Answer

have you been asked to use any particular method?
e.g. iteration, Newton-Raphson, etc...

anonymous · Answer

no. I thought can use the logarithm rules to solve it. Is it possible?

asnaseer · Answer

no - not with logs alone as you would end up with:$$\log(3-3^x)=\log(5^x)=x\log(5)$$and there is no way to simplify $\log(3-3^x)$. The only way I know uses iterations to converge to the value.

asnaseer · Answer

A simple iterative way to solve this would be to rearrange it as follows:$$x_{n+1}=\frac{\log(3-3^{x_n})}{\log(5)}$$then start with, say, $x_0=0$ and work out $x_1$. plug this back in to work out $x_2$ and keep going until you converge to a solution.

anonymous · Answer

ok then. Thank you very much.

asnaseer · Answer

yw

anonymous · Answer

A numerical approximation is x=0.297324