If log10y = 0.5log10x+2, how do I get the explicit expression in terms of x and y?

Answer 1

let log = log base 10 in the following:-
log y = (1/2) log x + 2
log y = log x^(1/2) + log 100
y = 100 x^(1/2)
y = 100√x

Answer 2

I assume that log is to the base 10.

log10y = 0.5log10x+2
=> log 10 + log y = 0.5 log 10 + 0.5 log x + 2
=> 1 + log y = 0.5 + log √x + 2
=> log y - log √x = 1.5
=> log (y / √x) = 1.5
=> y / √x = 10^(1.5)
=> y = [10^(1.5)] √x