07 - Exponential, Logarithmic And Modulus Functions

St Joseph’s Institution Secondary Four Mathematics TOPIC − Exponential, Logarithmic and Modulus Functions Name:_____________________________________ ( Q1)

Q2)

Solve the following equations a) ( 2.5) x −3 = 0.4 x b)

(2

c)

9 x − 4 = 3 x +1

d)

2e 2 x +1 = e x +1 + 15e

e)

log 2 (1 + x ) + log 2 ( 5 − x ) − log 2 ( x − 2) = 3

f)

( log5 x ) 2 − 3 log5 x + 2 = 0

g)

lg 4 x − 4 − x lg 2 = lg 3

h)

log9 [ log 2 ( 4 x − 16 ) ] = log16 4

i)

log 4 x − log x 8 =

j)

( lg x ) lg x

k)

3 x − 2 = 2x

l)

e 2 ln x + ln e 2 x = 8

3 x +2

)(3 ) = 16

(

x −1

)

1 2

= x where ( x > 1)

( )

Given that p = log 4 x , find, in terms of p, x i) ii) iii)

Q3)

) Class: ___________

Simplify

© Jason Ingham 2009

log x

1 64

iv)

1 1 − n −m . m −n 1− x x −1

1

log 2 x log16 256 x

Q4)

Solve the following equations 35x 1 = a) x x 9 27

(

b)

Q5)

( )

2 2 y +1 + 32 = 16 2 y

In an investment of a savings fund, the money invested increased with time. A man invested $50000 and the value of his investments, $S, after t years, is given by S = 5000 ln( 2t + 3 ) . Find i) the amount of money he will get after 5 years of investment, ii)

Q6)

)

the number of years needed for his investment to triple.

 1   , x > 1 . Insert in your sketch the Sketch the graph of y = ln  x −1 additional graph required to illustrate how a graphical solution to the equation x = e 8 −4 x + 1 may be obtained. x − 1 , showing clearly the point(s) of intercept y along the axes and the coordinates of the stationery point(s).

Q7)

Sketch the graph of y = 2 −

Q8)

Show that

Q9)

3 Given that log p xy = m and log p

1 log x xy

(

+

1 . log y xy = 1

)

and n.

2

y x

= n , express log p

p3 in terms of m xy