Starter
Simplify
1)
10
32 x
÷ 4x
4
=
2)
(16 x 4 ) 0.5 =
3)
3
27a12 =
Write these in surd form
4)
x
2
7
5)
2
3
(27x)
2
5
6)
x
9)
83 x
Write these in index form
7)
3
x10
8)
4
625 x12
HW Theta pg 32 & 33 Done?
4
Expressing numbers as powers of the same base
9
5
 
 3
2 5
3
10
Use the rule  x 
a b
95

2
27
so
 5

2

Theta
Ex 8.06
 x ab to rewrite the powers with a common base
Express the following as a power of 3
Express the following as a power of 9
1) 27 =
4) 6561 =
2) 243 =
1
5) 81 
Solve these equations
7)
3 x  243
Simplify
64x n
3n
10)
4

5n
2
2 x  8x  4
8)
11)
2
6n 2
x
n 1
9)
3 x  3  9 x 1
16 m 1 3x 

4 m m 1 m  3
2 9 x
m

12)
3)
6)
1

81
1
3

. Logarithms: What do you notice? .
Ex 9.01
Write the equivalent index statement
1) Log39 = 2
32 = 9
2) Log416 = 2
42 = 16
3) Log5125 = 3
53 = 125
4) Log99 = 1
91 = 9
5) Log101000 = 3
103 = 1000
6) Log3243 = 5
35 = 243
Find the value of ‘w’ in each of:
7) Log3w = 4
w = 81
8) Log6w = 5
w = 7776
9) Log2256 = w
w=8
10) Log32187 = w
w=7
11) Logw27 = 3
w=3
12) Logw729 = 3
w=9
Logarithms
Logarithms were invented by John Napier in 1614. They were initially used to solve
complex multiplication and division problems.
Logs get at the power…
24 = 16
is equivalent to
Index equation
log2 16  4
Log equation
log2 16  4 means
“what is the power on 2 which gives a result of 16? Answer = 4”
Said as “Log base 2 of 16 is 4” or “Log of 16 to the base 2”
The most common logs used are to the base 10 and e (e = 2.71828182845905…)
On the calculator these are the Log (log base 10) and Ln (log base e) functions
10 3  1000
Log10 1000  3
2 5  32
Log2 32  5
Logs Skills
Skills:
Convert between index equation and log equation
1)
28 = 256
2)
log3 243  5
4)
log1 0 10000
6)
logx 15625 6
Calculate logs
3)
log2 1024 
Solve log equations
5)
log4 x  5
HW Theta pg 34 & 35
Theta
Ex 9.01