Use properties of logarithms to expand the logarithmic expre

Use properties of logarithms to expand the logarithmic expression as much as possible. Evaluate logarithamic log squareroot 10,000 t

Solution

log(10000t)

==> log (10000t)^1/2      

==> (1/2) log (10000t)    since ln a^b = b lna

==> (1/2) [ log10000 + logt]     since log(ab) = loga + logb

==> (1/2) [ log10⁴ + logt]  

==> (1/2) [ 4 log10 + logt]         since log a^b = b log a

==> (1/2) [ 4 (1) + logt]             since log_a a = 1

==> (1/2)[4 + logt]

==> 2 + (1/2) logt

Hence log(10000t) = 2 + (1/2) logt