Repost from Brilliant: Can anyone solve this?

"Define $f_a^b(x)$ as a function which converts $x$ into base $a$ and then interprets it as a number in base $b$.

For example, $f_2^{10}(0.5)$ will mean first changing $0.5$ to base $2$ i.e. $0.1$ and then interpreting $0.1$ as a base $10$ number. That's it!

So, find a general formula for $\displaystyle \int_0^1 f_a^b(x)~\mathrm dx$"

Question

Repost from Brilliant: Can anyone solve this?

"Define $f_a^b(x)$ as a function which converts $x$ into base $a$ and then interprets it as a number in base $b$.

For example, $f_2^{10}(0.5)$ will mean first changing $0.5$ to base $2$ i.e. $0.1$ and then interpreting $0.1$ as a base  $10$ number. That's it!

So, find a general formula for $\displaystyle \int_0^1 f_a^b(x)~\mathrm dx$"

astrophysics · Answer

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geerky42 · Answer

geerky42 · Answer

@Astrophysics Maybe you want to leave mark on new question?

astrophysics · Answer

Haha thanks!