3^x+1 = 4^x-1

Question

3^x+1 = 4^x-1

anonymous · Answer

3^x+1-4^x=-1 . You see hhow that works?

anonymous · Answer

yes...

anonymous · Answer

$$2=4^x-3^x$$ which is $$4^x-4^{\log_4(3)x}=2$$Taking the log of both sides, we get$$\log_4(4^x-4^{\log_4(3)x})=\log_4(2)$$Which is$$x-x\log_4(3)=\frac{1}{2}$$In end, we get$$x(1-\log_4(3))=0.5$$I feel you can do the rest.

anonymous · Answer

0.116?

anonymous · Answer

final answer that is

anonymous · Answer

Wait, don't take that, I screwed up, somewhere, it's not adding up correctly.

anonymous · Answer

No, there's no nice closed form solution, I don't think. This must be a graphing problem, because we can't even turn this into a set of series or anything. Damn, this is ridiculously difficult, actually.

anonymous · Answer

Yeah, I dropped the log without justification, that's not right, but the answer is roughly $$x\approx1.327$$

anonymous · Answer

A. 	
8.638
	B. 	
0.116
	C. 	
7.000
	D. 	
0.143

anonymous · Answer

those were the options for answers

anonymous · Answer

That's funky, since $$4^{1.33}\approx6.3202$$And$$3^{1.33}\approx4.3109$$Which is$$4^{1.33}-3^{1.33}\approx2.0094$$Is the problem typed up correctly?