Question 1

Solve the equation

log₉ ( x  + 3 )= Log₃2

Question 2

Solve for p:

4^{4p + 1}   x 16  /  64^{p + 1}   = 1/256

Question 3

Solve the simultaneous equations :-

5^{2m - 3}   x 25^{p + 1}   = 125

4^{-2m - 3}   x 25^{6-3p + 1}   = 1

where m and p are constants

Question 4

Show  that log₆ xy = 2Log₃₆x +  2Log₃₆y  .Hence or otherwise, find the values of x and y that satisfy the equations

log₆ xy = 5 and log₃₆x / log₃₆y = 3/2

Question 5

Given that m=3^x and n =3^x , express log₂₇ m - log₉n in terms of x and y

Question 6

Given that 2log₆ ( x  + y )= 2 + Log₆x +  Log₆y show that

x² + y² = 14xy

Question 7

Without using calculator / logarithm tables, Solve the equation

 log₁₆ [ Log₄(7x-228) ] = Log₄₉7

Question 8

9log_x9 -log₉9x²= 18

Question 9

log₉x + log₉2x= 3/2

Question 10

log_x (2x² -9x + 20) = 2

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