Surds Indices And Log Rules

Question 1

Surds n{ab

Answer 1

n{a x n{b

Question 2

Surds n{a/b

Answer 2

n{a / n{b

Question 3

m{n{a
Surd in a surd

Answer 3

mn{a

Question 4

a^m/n

Answer 4

(n{a)^m = n{a^m

Question 5

Rationalising denominator SURDS

Answer 5

eg 1/2-{2
x 2+{2 / 2+{2
so it’s technically multiplying it by one
just opposite sign of the denominator both on top and below

Question 6

How to solve when {a = b

Answer 6

Square both sides lol

Question 7

Equality property of Surds

Answer 7

a + b{k = c + d{k

a = c
b = d

Sub in and check and reject some

Question 8

(ab)^n

Answer 8

= a^n b^n

Question 9

a^-1

Answer 9

= 1/a^n

Question 10

a^1/n

Answer 10

n{a

Question 11

lg xy

Answer 11

lg x + lg y

Question 12

lg x/y

Answer 12

logx - logy

Question 13

loga b —> logb a

Answer 13

= 1 / logb a

Question 14

loga b
Base change

Answer 14

logc b / logc a

Question 15

Loga 1

Answer 15

0

Question 16

Loga a

Answer 16

1

Question 17

loga 1/b OR log1/b a

Answer 17

-loga b

Question 18

loga b x logb c

Answer 18

loga c

Question 19

Basic log conversion from exponential form to logarithmic form

Answer 19

y = b^x
(Criss cross)
x = logb y