Solve log_{3}frac{3sqrt{3}}{sqrt{3}}

$$\log _ { 3 } \frac { 3 \sqrt { 3 } } { \sqrt { 3 } }$$

Evaluate

$$1$$

Solution Steps

Rationalize the denominator of \frac{3\sqrt{3}}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\log_{3}\left(\frac{3\sqrt{3}\sqrt{3}}{\left(\sqrt{3}\right)^{2}}\right)$$

The square of \sqrt{3} is 3.

$$\log_{3}\left(\frac{3\sqrt{3}\sqrt{3}}{3}\right)$$

Multiply \sqrt{3} and \sqrt{3} to get 3.

$$\log_{3}\left(\frac{3\times 3}{3}\right)$$

Multiply 3 and 3 to get 9.

$$\log_{3}\left(\frac{9}{3}\right)$$

Divide 9 by 3 to get 3.

$$\log_{3}\left(3\right)$$

The base 3 logarithm of 3 is 1.

$$1$$

Factor

$$1$$