Exponentials, Logarithms, and Quadratics

Convert between exponential and logarithm

100

Convert to a logarithm

5²=25

log₅25 = 2

200

Convert to an exponential equation.

log₄64 = 3

4³ = 64

300

Convert to a logarithm and solve for x.

3^x = 81

log₃81 = x

x = 4

400

Convert to an exponential equation and solve for x.

log₅625 = x

5^x = 625

x = 4

500

Convert to a logarithm and solve for x

x⁵ = 243

log_x243 = 5

x = 3

Calculate the Logarithm

100

log₁₀1,000,000 = x

x = 6

200

log₂8=x

x=3

300

log₁₀x = 5

x = 100,000

400

log₃x=2

x = 9

500

log_x16 = 4

x = 2

Convert to Standard Form

100

(x+3)(x+4)

x² + 7x + 12

200

(x-5)(x+3)

x² - 2x - 15

300

(x-4)²

x² - 8x + 16

400

(3x+5)(4x+3)

12x² + 29x + 15

500

(4x-5)(5x+5)

20x² - 5x - 25

Identifying Intercepts

100

What is/are the x-intercept(s)?

(x-3)(x-2)

(3,0) and (2,0)

200

What is/are the x-intercept(s)?

(x+3)(x-5)

(-3,0) (5,0)

300

What is the y-intercept?

16x² - 212x + 15

(0,15)

400

What is/are the x-intercepts?

x(2x+4)

(0,0) (-2,0)

500

What is the y-intercept?

(2x+3)(3x-4)

(0,-12)