Solve log_{6}6quadtext{(b)}log_{4}1/64

$$\log _ { 6 } 6 \quad \text { (b) } \log _ { 4 } \frac { 1 } { 64 }$$

Evaluate

$$-3b$$

Solution Steps

The base 6 logarithm of 6 is 1.

$$1b\log_{4}\left(\frac{1}{64}\right)$$

The base 4 logarithm of \frac{1}{64} is -3.

$$1b\left(-3\right)$$

Multiply 1 and -3 to get -3.

$$-3b$$

Differentiate w.r.t. b

$$-3$$

Steps Using Definition of a Derivative

The base 6 logarithm of 6 is 1.

$$\frac{\mathrm{d}}{\mathrm{d}b}(1b\log_{4}\left(\frac{1}{64}\right))$$

The base 4 logarithm of \frac{1}{64} is -3.

$$\frac{\mathrm{d}}{\mathrm{d}b}(1b\left(-3\right))$$

Multiply 1 and -3 to get -3.

$$\frac{\mathrm{d}}{\mathrm{d}b}(-3b)$$

The derivative of ax^{n} is nax^{n-1}.

$$-3b^{1-1}$$

Subtract 1 from 1.

$$-3b^{0}$$

For any term t except 0, t^{0}=1.

$$-3$$