Solve fquadlg(1000/sqrt{10})

$$f \quad \lg ( \frac { 1000 } { \sqrt { 10 } } )$$

Evaluate

$$\frac{5f}{2}$$

Solution Steps

Rationalize the denominator of \frac{1000}{\sqrt{10}} by multiplying numerator and denominator by \sqrt{10}.

$$f\log(\frac{1000\sqrt{10}}{\left(\sqrt{10}\right)^{2}})$$

The square of \sqrt{10} is 10.

$$f\log(\frac{1000\sqrt{10}}{10})$$

Divide 1000\sqrt{10} by 10 to get 100\sqrt{10}.

$$f\log(100\sqrt{10})$$

Differentiate w.r.t. f

$$\frac{5}{2} = 2\frac{1}{2} = 2.5$$