91Ó°ÊÓ

Use the properties of logarithms to rewrite each logarithm if possible. Assume that all variables represent positive real numbers. $$\log _{6}(7 m+3 q)$$

The given function \(f\) is one-to-one. Find \(f^{-1}(x)\). $$f(x)=5 x^{3}-7$$

$$\text { Solve each formula for the indicated variable.}$$ $$A=T_{0}+C e^{-k}, \text { for } k$$

Use the properties of logarithms to rewrite each logarithm if possible. Assume that all variables represent positive real numbers. $$\log _{k} \frac{p q^{2}}{m}$$

Decide which of the two plans will provide a better yield. (Interest rates stated are annual rates.) Plan A: \(\$ 40,000\) invested for 3 years at \(2.5 \%,\) compounded quarterly Plan B: \(\$ 40,000\) invested for 3 years at \(2.4 \%,\) compounded continuously

$$\text { Solve each formula for the indicated variable.}$$ $$y=\frac{K}{1+a e^{-b x}}, \text { for } b$$

Decide which of the two plans will provide a better yield. (Interest rates stated are annual rates.) Plan A: \(\$ 50,000\) invested for 10 years at \(4.75 \%,\) compounded daily \((n=365)\) Plan B: \(\$ 50,000\) invested for 10 years at \(4.7 \%,\) compounded continuously

Use the properties of logarithms to rewrite each logarithm if possible. Assume that all variables represent positive real numbers. $$\log _{2} \frac{x^{5} y^{3}}{3}$$

The given function \(f\) is one-to-one. Find \(f^{-1}(x)\). $$f(x)=4-3 x^{3}$$

The given function \(f\) is one-to-one. Find \(f^{-1}(x)\). $$f(x)=\frac{x}{4+3 x}$$