Exponents/Logarithms Review

Exponents

100

(8x^3y^5)/(24x^4y

y^4/(3x)

200

(2x^2y^-3)

(2x^2)/y^3

300

(2x^-2y^3)^3

(8y^3)/x^6

400

((2x^2y^-3)/(3x^-3y^4))^-2

(9y^14)/(4x^10)

500

(4x^-3y^5)^(-1/2)

x^(3/2)/(2y^(5/2))

Logarithms

100

log₂(8)

3

200

ln(1)

0

300

log₃(1/81)

-4

400

ln(e)

1

500

log(10^3)

3

Properties

100

log((x^2y)/z)

2log(x)+log(y)-log(z)

200

1/2log(x)-1/3log(y)

log((sqrtx)/(3sqrty))

300

2log₁₀(5)+log₁₀(4)

2

400

log₄(3)-log₄(48)

-2

500

log₂(M)+log₂(N)+3

log₂(8MN)

Change of Base

100

log₂9

log₁₀(9)/log₁₀(2)

200

log₄(8)

log₁₀(8)/log₁₀(4)

300

log₃(54)

log₁₀(54)/log₁₀(3)

400

log₃(50)

log₁₀(50)/log₁₀(3)

500

logpi(e)

log(e)/logpi