Question

Condense the expression into a

single logarithm and simplify.

2(log 18 - log 3) + 1/2 log 1/16

Answer 1

1.556 or
`\mathrm{2\log _(10)\left(6\right)}`

Explanation:

`2\left(\log _(10)\left(18\right)-\log _(10)\left(3\right)\right)+(1)/(2)\cdot (\log _(10)\left(1\right))/(16)\\\log _(10)\left(18\right)-\log _(10)\left(3\right)\\ = 18 / 3\\= 6\\= log_(10)(6)\\\\\log _(10)\left(18\right)-\log _(10)\left(3\right) = log_(10)(6)\\\\(1)/(2) \cdot(\log _(10)\left(1\right))/(16)\\log_(10)(1) = 0\\= (1)/(2) \cdot(0)/(16)\\\\0 / 16 = 0\\a \cdot 0 = 0\\= 0\\\\= 2\log _(10)\left(6\right)+0\\=2\log _(10)\left(6\right)`

Hope this helps!

Answer 2

`2(\log 18-\log 3)+\frac 12 \log (1)/(16)=2 \log (18)/(3)+\log \sqrt{(1)/(16)}\\=2 \log 6+\log (1)/(4)=\log 6^2+\log (1)/(4)=\log 36+\log (1)/(4)\\=\log (36)/(4)=\log 9`