f4 maths(2 questions)

log√(2/27)
=log (2/27)^(1/2)
=(1/2) log (2/27)
= (1/2) [log 2 - log 27]
= (1/2) [log (10/5) - log 3^3]
= (1/2)[log 10 - log 5 - 3log3]
= (1/2)[1-b-3a]
=(1-b-3a)/2
2. (1/2)log x=2+log y
log [x^(1/2)] = log 100 + log y
log[x^(1/2)] = log 100y
x^(1/2) = 100y
x = (100y)^2
x = 10000y^2

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1)If log3=a and log5=b,express each of the following in terms of a and b.

log√(2/27)
= (1/2) log (2/27)
= (1/2) (log 2 - log 27)
= (1/2) (log 2 - log (3^3))
= (1/2) (log 2 - 3 log 3)
= (1/2) (log (10/5) - 3 log 3)
= (1/2) (log 10 - log 5 - 3 log 3)
= (1/2) (1 - b - 3a)
= (1 - b - 3a)/2

2)In each of the following,express x in terms of y.

(1/2)log x=2+log y
=> log x^(1/2) = 2 log 10 + log y
=> log x^(1/2) = log 10^2 + log y
=> log x^(1/2) = log (10^2 y)
=> x^(1/2) = 100y
=> x = (100y)^2
= 10000y^2