Key: logx= log base x

Question

1. Prove that:
(logx64 +logx4 -logx8)/(logx1024) =1/2

2.factorize by grouping

r^2s^2+3t^2+r^2t^2+3s^2

3.factorize the following expression

49p^2-1/25

4.simplify

i.(ax+bx+ay+by)/(cx+cy+dx+dy)

ii.(3/4+1/2) / (1/3+1/2)

5.two thirds of a number together with a quarter of the same number and a sixth of that number equal 52.calculate the number

Answer 1

Hints:
1.
Use basic laws of logarithm:
log(a)+log(b)=log(ab)
log(a)-log(b)=log(a/b)
log(a^b)=b(log(a))
and use the fact that all the numeric values are powers of 2:
2^6=64
2^2=4
2^3=8
2^10=1024

2.
I'll get you started:
r^2s^2+3t^2+r^2t^2+3s^2
=(r^2s^2+r^2t^2)+(3t^2+3s^2 )
take out common factors in each group enclosed in parentheses and continue factoring.

3.
Hint: expression is difference of two squares.
See for example:
http://www.regentsprep.org/regents/math/algebra/AV6/Lfactps.htm

4.
i. factorize numerator and denominator by grouping, and cancel common factors.
ii. do the sums of fractions and simplify.

5.
Let the unknown number be x.
Then interpret the question in terms of x. Solve for x.