Chapter 18

Convert to logarithmic form. $$3^{4}=81$$

Find the value of \(x\) in each expression. $$x=\log _{3} 9$$

Graph each exponential function, manually or by calculator, for the given values of \(x\) Take \(e=2.718\).$$y=0.2(3.2)^{x} \quad(x=-4 \text { to }+4)$$

Solve for \(x\) to three significant digits. $$2^{x}=7$$

Convert to logarithmic form. $$5^{3}=125$$

Find the value of \(x\) in each expression. $$x=\log _{2} 8$$

Graph each exponential function, manually or by calculator, for the given values of \(x\) Take \(e=2.718\).$$y=3(1.5)^{-2 x} \quad(x=-1 \text { to } 5)$$

Solve for \(x\) to three significant digits. $$(7.26)^{x}=86.8$$

Convert to logarithmic form. $$4^{6}=4096$$

Find the value of \(x\) in each expression. $$x=\log _{8} 2$$

Graph each exponential function, manually or by calculator, for the given values of \(x\) Take \(e=2.718\).$$y=5\left(1-e^{-x}\right) \quad(x=0 \text { to } 10)$$

Solve for \(x\) to three significant digits. $$(1.15)^{x+2}=12.5$$

Convert to logarithmic form. $$7^{3}=343$$

Find the value of \(x\) in each expression. $$x=\log _{9} 27$$

Graph each exponential function, manually or by calculator, for the given values of \(x\) Take \(e=2.718\).$$y=4 e^{x / 2} \quad(x=0 \text { to } 4)$$

Solve for \(x\) to three significant digits. $$(2.75)^{x}=(0.725)^{x^{2}}$$

Write as the sum or difference of two or more logarithms. $$\log \frac{x}{2}$$

Convert to logarithmic form. $$x^{5}=995$$

Find the value of \(x\) in each expression. $$x=\log _{27} 9$$

Solve for \(x\) to three significant digits. $$(15.4)^{\sqrt{x}}=72.8$$

Convert to logarithmic form. $$a^{3}=6.83$$

Find the value of \(x\) in each expression. $$x=\log _{4} 8$$

Find the amount to which \(\$ 500 dollars will accumulate in 6 years at a compound interest rate of \)6 \%$ per year compounded annually.

Solve for \(x\) to three significant digits. $$e^{5 x}=125$$

Convert to exponential form. $$\log _{10} 100=2$$

Find the value of \(x\) in each expression. $$x=\log _{8} 4$$

Solve for \(x\) to three significant digits. $$5.62 e^{3 x}=188$$

Write as the sum or difference of two or more logarithms. $$\log \frac{3 x}{4}$$

Convert to exponential form. $$\log _{2} 16=4$$

What annual compound interest rate (compounded annually) is needed to: enable an investment of \(\$ 5000 dollars to accumulate to \)\$ 10,000 dollars in 12 years? Use \(\mathrm{Eq}\) \(1009, y=a(1+n)^{t}\).

Find the value of \(x\) in each expression. $$x=\log _{27} 81$$

Solve for \(x\) to three significant digits. $$1.05 e^{4 x+1}=5.96$$

Write as the sum or difference of two or more logarithms. $$\log \frac{5}{x y}$$

Convert to exponential form. $$\log _{5} 125=3$$

Find the value of \(x\) in each expression. $$\log _{x} 8=3$$

Solve for \(x\) to three significant digits. $$e^{2 x-1}=3 e^{x+3}$$

Write as the sum or difference of two or more logarithms. $$\log \frac{1}{2 x}$$

Convert to exponential form. $$\log _{4} 1024=5$$

Find the value of \(x\) in each expression. $$\log _{3} x=4$$

Solve for \(x\) to three significant digits. $$14.8 e^{3 x^{2}}=144$$

Write as the sum or difference of two or more logarithms. $$\log \frac{2 x}{3 y}$$

Convert to exponential form. $$\log _{3} x=57$$

Find the value of \(x\) in each expression. $$\log _{x} 27=3$$

Write as the sum or difference of two or more logarithms. $$\log \frac{a b c}{d}$$

Solve for \(x\) to three significant digits. $$5^{2 x}=7^{3 x-2}$$

Convert to exponential form. $$\log _{x} 54=285$$

Find the value of \(x\) in each expression. $$\log _{x} 16=4$$

Write as the sum or difference of two or more logarithms. $$\log \frac{x}{2 a b}$$

Solve for \(x\) to three significant digits. $$3^{x^{2}}=175^{x-1}$$

Use either the formulas or the universal growth and decay curves, as directed by your instructor.A quantity grows exponentially at the rate of \(5.00 \%\) per year for 7 years. Find the final amount if the initial amount is 201 units.