Simple log problem

[courtrigrad]

Hello,

I need help with this problem:


4^x + 4^-x = 5/2

My Solution: (Assume we use log with base 4)

log ( 4^x + 4^-x) = log(5/2)

= log (4^0) = log (5/2) ????


I dont see what I am doing wrong. I used the Product Rule. Any help would be greatly appreciated.

Thanks

[Pyrrhus]

How about this

(4^x)(4^x) + (4^-^x)(4 ^x) = \frac{5}{2}(4^x)

Maybe i should arrange

(4^x)^2 + 1 = \frac{5}{2}(4^x)

x= 4^x

x^2 + 1 = \frac{5}{2}x

[Leong]

\begin{multline*}
\begin{split}
&log(AB)=log\ A+log\ B\\
&There\ isn't\ anything\ like\ this:\\
&log(A+B)=log(AB)\\
&4^x+4^{-x}=4^x+\frac{1}{4^x}=\frac{4^{2x}+1}{4^x}\\
&4^x*4^{-x}=4^{x-x}=1\\
\end{split}
\end{multline*}

[recon]

How about this

(4^x)(4^x) + (4^-^x)(4 ^x) = \frac{5}{2}(4^x)

Maybe i should arrange

(4^x)^2 + 1 = \frac{5}{2}(4^x)

x= 4^x

x^2 + 1 = \frac{5}{2}x

x= 4^x should not be used. I see where you are going here. But this is wrong. Instead we should assign it to a different variable like y= 4^x . So,

y^2 + 1 = \frac{5}{2}y

[Pyrrhus]

It's true, i was just reminding him of Ax^2 + Bx + C, but thanks for pointing it out.