Solve log_{2}(1/32)4x

$$\log _ { 2 } ( \frac { 1 } { 32 } ) 4 x$$

Evaluate

$$-20x$$

Solution Steps

The base 2 logarithm of \frac{1}{32} is -5.

$$-5\times 4x$$

Multiply -5 and 4 to get -20.

$$-20x$$

Differentiate w.r.t. x

$$-20$$

Steps Using Definition of a Derivative

The base 2 logarithm of \frac{1}{32} is -5.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-5\times 4x)$$

Multiply -5 and 4 to get -20.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-20x)$$

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

$$-20x^{1-1}$$

Subtract 1 from 1.

$$-20x^{0}$$

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

$$-20$$