Use properties of logarithms or a definition to simplify eac

Use properties of logarithms or a definition to simplify each expression. Check each result with a change-of-base formula.

(a) log₃ 9

(b) log7 (1/7)

Solution

Use the laws of logarithm : logz(x) = logx/logz

a) log3(9) = log9/log3

= log3^2/log3

=2log3/log3

= 2

log7(1/7)

log(1/7)/log7

log(7^-1)/log7

-1(log7/log7)

= -1