plz help me with this logartihm question:

 

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given that..... log xy = 2 log x + 2

 

determine the value of y for the following without using a calculator

x = 3, 5, 10, 12

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btw, i think the left side of the equation is actually: logx multiplied by y

and not: log (xy)

 

plz help!!

OK well if the left side is y * log x, then the formula simplifies to the following,

 

log (x^y) = log (2x^2) -->

 

2 x^2 = x^y, therefore

 

y = log(2 x^2)/ log(x)

 

so for x =3 y = log 18 / log 3

5 --> log 50 / log 5

10 --> log 200 / log 10

12 --> log 288 / log 12

 

if it's the other way around and it is log (x y), then

 

y = 2x

3 -> y = 6

5 -> y =10

10 -> y =20

12 -> y = 24