Solve log_{3}27+log_{1/2}4-2log1,1/9

$$\log _ { 3 } 27 + \log _ { \frac { 1 } { 2 } } 4 - 2 \log 1 , \frac { 1 } { 9 }$$

Sort

$$\frac{1}{9},1$$

Solution Steps

The base 3 logarithm of 27 is 3.

$$sort(3+\log_{\frac{1}{2}}\left(4\right)-2\log(1),\frac{1}{9})$$

The base \frac{1}{2} logarithm of 4 is -2.

$$sort(3-2-2\log(1),\frac{1}{9})$$

Subtract 2 from 3 to get 1.

$$sort(1-2\log(1),\frac{1}{9})$$

The common logarithm of 1 is 0.

$$sort(1-2\times 0,\frac{1}{9})$$

Multiply 2 and 0 to get 0.

$$sort(1-0,\frac{1}{9})$$

Subtract 0 from 1 to get 1.

$$sort(1,\frac{1}{9})$$

Convert decimal numbers in the list 1,\frac{1}{9} to fractions.

$$1,\frac{1}{9}$$

To sort the list, start from a single element 1.

$$1$$

Insert \frac{1}{9} to the appropriate location in the new list.

$$\frac{1}{9},1$$

Evaluate

$$1,\frac{1}{9}$$