Log function identity/exponential function.?

Question

I didn't know what to title this, but I basically need to know the answers to the following:

10^log10·[square root of 2]

^^ in case you can't read it, it's 10 to the power of log10 andthe log 10 is multiplied by the square root of 2.

the second problem is

exp10(log10(pi))

if somebody could explain this, i know it involves the identity function. thanks!

Answer 1

Number = base^log.

Therefore, using square brackets to enclose bases and round brackets to enclose arguments:

10^( log[10](x) ) = x.

Putting x = sqrt(2):

10^( log[10]( sqrt(2) ) ) = sqrt(2).

I'm not sure whether I am interpreting the second question correctly. I feel some clarification of your notation is needed. Is it:

e^( 10 * log[10] (pi) ) (a bit tricky)

or

exp[10] ( log[10](pi) )

meaning presumably

10^( log[10] (pi) ), which equals pi?