Express log(9/16) + log (4/16) as the difference of the logarithms of two integers.

Answer 1

log(a/b) = loga - logb

log(ab) = loga + logb

log(9/16) + log(4/16)

=log(9/16) + log(1/4)

=log((9/16)(1/4))

=log(9/(16)(4))

=log(9/64)

=log9 - log64

or

log(9/16) +log(4/16)

= log9 - log16 + log4 - log16

= log(9x4) - 2log16

= log36 -log(16^2)

= log36 - log256

log36 =about 1.56

log256 = about 2.41

1.56-2.41 = -0.85

log(9/16)= about -0.25

log(4/16) = about -0.60

-.25-.6 = -0.85

log9 = about 0.954

log64 = about 1.806

.954- 1.806= -0.852