Solve blog_{2}8^15

$$b \log _ { 2 } 8 ^ { 15 }$$

Evaluate

$$45b$$

Solution Steps

Calculate 8 to the power of 15 and get 35184372088832.

$$b\log_{2}\left(35184372088832\right)$$

The base 2 logarithm of 35184372088832 is 45.

$$b\times 45$$

Differentiate w.r.t. b

$$45$$

Steps Using Definition of a Derivative

Calculate 8 to the power of 15 and get 35184372088832.

$$\frac{\mathrm{d}}{\mathrm{d}b}(b\log_{2}\left(35184372088832\right))$$

The base 2 logarithm of 35184372088832 is 45.

$$\frac{\mathrm{d}}{\mathrm{d}b}(b\times 45)$$

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

$$45b^{1-1}$$

Subtract 1 from 1.

$$45b^{0}$$

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

$$45\times 1$$

For any term t, t\times 1=t and 1t=t.

$$45$$