Exploring Logarithmic and Exponential Functions

Evaluate: log_2(8)

• 6

• 4

• 2

• 3

Convert to logarithmic form: 3^x = 27

• log_3(9) = x

• log_3(3) = x

• log_3(81) = x

• log_3(27) = x

Apply the law: log_a(bc) = ?

• log_a(b) - log_a(c)

• log_a(b) * log_a(c)

• log_a(bc) + log_a(a)

• log_a(b) + log_a(c)

Solve for x: 5^x = 125

• 5

• 4

• 3

• 2

Graph the function: y = 2^x

• The graph of y = 2^x is a straight line that slopes downwards.

• The graph of y = 2^x is an exponential curve that rises steeply to the right and approaches the x-axis to the left.

• The graph of y = 2^x is a horizontal line that remains constant.

• The graph of y = 2^x is a parabolic curve that opens downwards.

Evaluate: log_10(1000)

• 2

• 3

• 4

• 5

Convert to exponential form: log_5(25) = 2

• 5^2 = 25

• 5^3 = 125

• 5^1 = 5

• 5^4 = 625

Apply the law: log_a(b/c) = ?

• log_a(b) / log_a(c)

• log_a(b) * log_a(c)

• log_a(b) - log_a(c)

• log_a(b + c)

Solve for x: 3^(2x) = 81

• 4

• 1

• 3

• 2

Graph the function: y = e^x

• The graph of y = e^x is a sinusoidal wave that oscillates between -1 and 1.

• The graph of y = e^x is a straight line that passes through (0,0) and decreases as x increases.

• The graph of y = e^x is an exponential curve that passes through (0,1) and increases rapidly as x increases.

• The graph of y = e^x is a quadratic curve that opens downwards and has a vertex at (0,1).