91Ó°ÊÓ

Solve each logarithmic equation. Express irrational solutions in exact form. $$ 3\left(\log _{7} x-\log _{7} 2\right)=2 \log _{7} 4 $$

Write each expression as a sum and/or difference of logarithms. Express powers as factors. \(\ln (e x)\)

How many years will it take for an initial investment of $$ 10,000\( to grow to $$ 25,000 ?\) Assume a rate of interest of 6 % compounded continuously.

Verify that the functions \(f\) and g are inverses of each other by showing that \(f(g(x))=x\) and \(g(f(x))=x\). Give any values of x that need to be excluded from the domain of \(f\) and the domain of g. $$ f(x)=\frac{2 x+3}{x+4} ; \quad g(x)=\frac{4 x-3}{2-x} $$

Solve each logarithmic equation. Express irrational solutions in exact form. $$ 2 \log _{13}(x+2)=\log _{13}(4 x+7) $$

Show that \((f \circ g)(x)=(g \circ f)(x)=x\) \(f(x)=x^{3} ; \quad g(x)=\sqrt[3]{x}\)

Write each expression as a sum and/or difference of logarithms. Express powers as factors. \(\ln \frac{e}{x}\)

How many years will it take for an initial investment of $$ 25,000\( to grow to $$ 80,000 ?\) Assume a rate of interest of 7 % compounded continuously.

Verify that the functions \(f\) and g are inverses of each other by showing that \(f(g(x))=x\) and \(g(f(x))=x\). Give any values of x that need to be excluded from the domain of \(f\) and the domain of g. $$ f(x)=\frac{x-5}{2 x+3} ; \quad g(x)=\frac{3 x+5}{1-2 x} $$

Find the domain of each function. $$ H(x)=\log _{5} x^{3} $$