Review of Basics

Page 1

EXPONENTS

x^a + x^b = x^(a+b)

(x^a)^b = x^ab

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

x^a + x^a = 2x^a

2^a + 2^a = 2^(a+1)

3^a +3^a = 2 * 3^a

3^a + 3^a + 3^a = 3 * 3^a = 3^(a+1)

LOGARITHMS

x^a = B -> log x B = a for x > 0

log a B = (log c B) / (log c A) for A, B, C > 0, A != 1

Let:

x = log c B

y = log c A

z = log a B

Z = X/Y

log a B = (log c B) / (log c A)

Then:

B = C^x

A = C^y

B = A^z

B = (C^Y)^Z = C^YZ = C^X

YZ = X

Z = X/Y