10^(1-x) = 6 ^(x)
I got:
log10 / log6 + log10 = x
or x = .562
$\displaystyle 10^{1-x} = 6^x$
$\displaystyle \Rightarrow \frac{10^1}{10^x} = 6^x$
$\displaystyle \Rightarrow 10 = 6^x \times 10^x$
$\displaystyle \Rightarrow 10 = 60^x $
$\displaystyle \Rightarrow x\ln60 = \ln 10$
$\displaystyle \Rightarrow x = \frac{\ln 10}{\ln60} = 0.5624$