91Ó°ÊÓ

Using the Change-of-Base Formula In Exercises \(11-14,\) evaluate the logarithm using the change-of-base formula. Round your result to three decimal places. $$\log _{3} 0.015$$

Solve for \(x.\) \(\log _{5} x=\frac{1}{2}\)

Approximate the point of intersection of the graphs of \(f\) and \(g .\) Then solve the equation \(f(x)=g(x)\) algebraically to verify your approximation. \(f(x)=2^{x}\) \(g(x)=8\)

Determine the time necessary for \(P\) dollars to double when it is invested at interest rate \(r\) compounded (a) annually, (b) monthly, (c) daily, and (d) continuously. r=10 \%

Evaluate the function at the indicated value of \(x\) without using a calculator. \(f(x)=\log _{2} x \quad x=64\)

Using Properties of Logarithms In Exercises \(15-20\) , use the properties of logarithms to rewrite and simplify the logarithmic expression. $$\log _{4} 8$$

Evaluate the function at the indicated value of \(x\) without using a calculator. \(f(x)=\log _{25} x \quad x=5\)

Approximate the point of intersection of the graphs of \(f\) and \(g .\) Then solve the equation \(f(x)=g(x)\) algebraically to verify your approximation. \(f(x)=\log _{3} x\) \(g(x)=2\)

Using Properties of Logarithms In Exercises \(15-20\) , use the properties of logarithms to rewrite and simplify the logarithmic expression. $$\log _{2}\left(4^{2} \cdot 3^{4}\right)$$

Using Properties of Logarithms In Exercises \(15-20\) , use the properties of logarithms to rewrite and simplify the logarithmic expression. $$\log _{5} \frac{1}{250}$$