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Winter vacations Worksheet Y1- HL

1.For what values of k will the following system of equations have a uniquesolution?

x+ 2y -3z = 5 ; 2x y z = 8 ; kx + y + 2z = 14

2.Express as a single log and then evaluate without using a calculator!a) log log20 5+ b) 6log2log212log 222 + d)2 6 2 2 2 33 3 3log ( log log ) +

3.Evaluate to 3sf:a) log 6 30 b) log 1/2 3

4.Solve: a) 2log162loglog23log 5555 =+ x x

b) 11 26412 =

x

c) 0834 = x x

d)ee x x x

4ln12lnln)52ln(ln2=++

5. 1261 )3(32

= x for all values of x

6.

Given that ab

bc

ca

loglog

log = :

a) find k and m in i) xk x 33

9 loglog = ii)

8log512log 327 m=

b) find all values of x for which 512logloglog 2733

921

=+ x x

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