Graduate from Honours Applied Mathematics with a specialization in Electrical Engineering
2. Express the following logarithms in terms of ln 5 and $\ln 7$a. $\ln (1 / 125)$ b. $\ln 9.8$c. $\ln 7 \sqrt{7}$d. $\ln 1225$e. $\ln 0.056$f. $(\ln 35+\ln (1 / 7)) /(\ln 25)$
Use the properties of logarithms to simplify the expressions in Exercises 3 and $4 .$a. $\ln \sin \theta-\ln \left(\frac{\sin \theta}{5}\right)$ b. $\ln \left(3 x^{2}-9 x\right)+\ln \left(\frac{1}{3 x}\right)$c. $\frac{1}{2} \ln \left(4 t^{4}\right)-\ln 2$
a. $$\ln \sec \theta+\ln \cos \theta$$b. $$\ln (8 x+4)-2 \ln 2$$c. $$3 \ln \sqrt[3]{t^{2}-1}-\ln (t+1)$$
In Exercises $5-36,$ find the derivative of $y$ with respect to $x, t,$ or $\theta,$ as appropriate.$$y=\ln 3 x$$
Find the derivative of $y$ with respect to $x, t,$ or $\theta,$ as appropriate.$$y=\ln 3 x$$
In Exercises $5-36,$ find the derivative of $y$ with respect to $x, t,$ or $\theta,$ as appropriate.$$y=\ln \left(t^{2}\right)$$