Question

1) use the properties of logarithms to simplify the logarithmic expression.

log base 10 (9/300)

log - log 300
log 9 = 2 log 3
log 300 = log 3 + log 100 = log 3+2

I just do not know how to put these together now!

Answer 1

log base 10 (9/300)
= log10 (3/100)
= log10(3) - log10(100)
= log10(3) - 2

Further simplification is not possible.

The numerical value is 0.47712 - 2
= -1.52288

Answer 2

log a b * log bc * logc a=1