Question

1/2log9+2log3-log6+log2-2.​

Answer 1

Answer:

1/2log9+2log3-log6+log2-2

=log(9^1/2)+log(3^2)-log6+log2-2

=log3+log9-log6+log2-2

=log[(3*9*2)/6]-2

=log9-2

=2log3-2

=2(log3-1)

Answer 2

Answer:

log 9/100

Step-by-step explanation:

1/2 log 9 + 2 log 3 - log 6 + log 2 - 2

= log 3^(2*1/2) + log 3^2 - log 6 + log 2 - 1 - 1

= log 3 + log 9 - log 6 + log 2 - log 10 - log 10       [ Since 1 = log 10 because log 10 is equal to 10^x=10 and x further equals to 1]

= log { ( 3 * 9 * 2) / (6 * 10 * 10) }   [ Using logarithms product law in which log x + log y = log x * y and also using division low in which log x - log y = log x / y]

= log { 54 / 600 }

= log (9 / 100)