Solve log_{3}27-1/log_{42}+log_{4}16

$$\log _ { 3 } 27 - \frac { 1 } { \log _ { 4 } 2 } + \log _ { 4 } 16$$

Evaluate

$$3$$

Solution Steps

The base 3 logarithm of 27 is 3.

$$3-\frac{1}{\log_{4}\left(2\right)}+\log_{4}\left(16\right)$$

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

$$3-\frac{1}{\frac{1}{2}}+\log_{4}\left(16\right)$$

Divide 1 by \frac{1}{2} by multiplying 1 by the reciprocal of \frac{1}{2}.

$$3-1\times 2+\log_{4}\left(16\right)$$

Multiply 1 and 2 to get 2.

$$3-2+\log_{4}\left(16\right)$$

Subtract 2 from 3 to get 1.

$$1+\log_{4}\left(16\right)$$

The base 4 logarithm of 16 is 2.

$$1+2$$

Add 1 and 2 to get 3.

$$3$$

Factor

$$3$$