General Math Rules

Log Rules

100

The product property:

ln(ab)

Ln(ab)=Ln(a)+ln(b)

200

The quotient property

ln(a/b)

Ln(a/b)=ln(a)-Ln(b)

300

The power property

ln(m)^p

ln(m)^p =pln(m)

400

Exponential and logarithmic

e^(lnx)

e^(lnx)=x

500

Inverse property

ln(e^x )

Ln(e^x)=x,x>0

600

One-to-one property of exponentials

if e^x =e^y

if e^x =e^y ,x=y

700

One-to-one property of logarithms

if lnx=lny

if lnx=lny, x=y

Dividing Rules and Factoring

100

(a/b)/c

(a/b)/c=a/(bc)

200

(a/b)/(c/d)

(a/b)/(c/d)=(a/(bc))/d=(ad)/(bc)

300

x^3+a^3

x^3+a^3=(x+a)(x^2-ax+a^2)

400

x^3-a^3

x^3-a^3=(x-a)(x^2+ax+a^2)

500

(x+a)^3

(x+a)^3=x^3+3ax^2+3a^2x+a^3

600

x^(2n)-a^(2n)

x^(2n)-a^(2n)=(x^n-a^n)(x^n+a^n)

700

Quadratic formula for

ax^2+bx+c=0

x=(-b+-sqrt(b^2 -4ac))/(2a)

Exponent Properties

100

a^na^m

a^na^m=a^(n+m)

200

(a^n)^m

(a^n)^m=a^(nm)

300

(a/b)^-n

(a/b)^-n=(b/a)^n=(b^n)/(a^n)

400

(a^n)/(a^m)

(a^n)/(a^m)=a^(n-m)=1/(a^(m-n))

500

(a/b)^n

(a/b)^n=(a^n)/(b^n)

600

1/(a^(-n))

1/(a^(-n))=a^n

700

a^(n/m)

a^(n/m)=(a^(1/m))^n=(a^n)^(1/m)

Properties of Complex Numbers

100

i

i=sqrt(-1)

200

i^2

i^2 =-1

300

sqrt(-a)

sqrt(-a)=isqrt(a)

400

(a+bi)(a-bi)

(a+bi)(a-bi)=a^2+b^2

500

|a+bi|

|a+bi|=sqrt(a^2+b^2)

600

overline(a+bi)

overline(a+bi)=a-bi

700

1/(a+bi)

1/(a+bi)=(a-bi)/((a+bi)(a-bi))=(a-bi)/(a^2+b^2)