Inverses and Logs

Find the Inverse

100

y = x² + 5

y = +- sqrt(x-5)

200

y = (2x+5)³

y = (cbrt(x) - 5) / 2

300

y = sqrt(-3x+4)

y = (x² - 4) / -3

400

y = -3x² + 1

y = +- sqrt((x/-3) - 1)

500

y = (1/4 x - 1)³

y = 4(cbrt(x) + 1)

Log. Equations

100

log₃(x) = 2

x = 9

200

log₂(x) = 3

x = 8

300

log₂(x) = 0

x = 1

400

log₃(x) = 1/2

x = sqrt(3)

500

log₂(x) = -1/2

x = 1/sqrt(2)

Logs & Inverses

100

Find the inverse of

f(x) = log(x)

f^-1(x) = 10^x

200

Find the inverse of 

f(x) = log₆(x+1) 

f^-1(x) = 6^x - 1

300

Find the inverse of

f(x) = 6^x

f^-1(x) = log₆(x)

400

Find the inverse of 

f(x) = log₇(x)

f^-1(x) = 7^x

500

Find the inverse of 

f(x) = 8^2x

f^-1(x) = 1/2 log₈(x)

OR

f^-1(x) = log₆₄(x)

Evaluate Logs

100

log₁₂144 = ?

? = 2

200

log₃ 27 = ?

? = 3

300

log₁₀(10000) = x

x = 4

400

log₆(1/36) = ?

? = -2

500

log₄(1/2) = ?

? = -2

Changing Forms

100

Write in Exponential form:

log₆(36) = 2

6² = 36

200

Write in Exponential Form:

log₄(2) = 1/2

4^1/2 = 2

300

Write in Log form:

4³ = 64

log₄(64) = 3

400

Write in Log. Form:

8^1/3 = 2

log₈(2) = 1/3

500

Write in Log form:

16^-1/2 = 1/4

log₁₆(1/4) = -1/2