Question

Type the correct answer in the box.
log 14/3+log 11/4 - log 22/15 = log

Answer 1

log(7)

Explanation:

Log Rules:

`\log(a \cdot b) =\log(a)+\log(b)\\\\\log\left( (a)/(b) \right) = \log(a) -\log(b)`

Given:

`\log\left( (14)/(3) \right) + \log\left( (11)/(5) \right)-\log\left( (22)/(15) \right)\\\\=\log(14)-\log(3)+\log(11)-\log(5)-\log(20)-(-\log(15))\\\\=\log(14)+\log(11)+\log(15)-\log(3)-\log(5)-\log(22)\\\\=\log(14)+\log(11)+\log(15)-(\log(3)+\log(5)+\log(22)) \\\\=\log\left( 14*11*15 \right) -\log\left( 3*5*22 \right) \\\\= \log\left( (14*11*15)/(3*5*22) \right) \\\\= \log\left( (14)/(2) \right) \\\\= \log\left( 7\right)`