Logarithms give us another method to write exponents. We can convert back and forth between exponential form and logarithmic form. When we want the exponential form, we are solving for the power. In the case of logarithmic form, we are solving for the exponent. In order to solve a logarithmic equation, we convert the equation into exponential form, then solve.

Test Objectives
• Demonstrate the ability to convert from exponential form to logarithmic form
• Demonstrate the ability to convert from logarithmic form to exponential form
• Demonstrate the ability to solve logarithmic equations
Logarithmic Functions Practice Test:

#1:

Instructions: Write each in logarithmic form.

a) $$2^6 = 64$$

b) $$81^{\frac{1}{2}} = 9$$

c) $$\sqrt[3]{125} = 5$$

d) $$10^{-3} = \frac{1}{1000}$$

#2:

Instructions: Write each in exponential form.

a) $$\log_{10}(10,000) = 4$$

b) $$\log_{11}\left(\frac{1}{121}\right) = -2$$

c) $$\log_{216}(6) = \frac{1}{3}$$

d) $$\log_{4}(256) = 4$$

e) $$\log_{1327}(1) = 0$$

#3:

Instructions: Solve each equation.

a) $$\log_{125}(25) = x$$

#4:

Instructions: Solve each equation.

a) $$\log_{x}(625) = 4$$

#5:

Instructions: Solve each equation.

a) $$\log_{x}(1024) = \frac{5}{2}$$

Written Solutions:

#1:

Solutions:

a) $$\log_{2}(64) = 6$$

b) $$\log_{81}(9) = \frac{1}{2}$$

c) $$\log_{125}(5) = \frac{1}{3}$$

d) $$\log_{10}\left(\frac{1}{1000}\right) = -3$$

#2:

Solutions:

a) $$10^4 = 10,000$$

b) $$11^{-2} = \frac{1}{121}$$

c) $$216^{\frac{1}{3}} = 6$$

d) $$4^4 = 256$$

e) $$1327^0 = 1$$

#3:

Solutions:

a) $$x = \frac{2}{3}$$

#4:

Solutions:

a) $$x = 5$$

#5:

Solutions:

a) $$x = 16$$