Quandaries and Queries


I'm a mature age university sudent in Western Australia and am studying externally. Its been a while since I last studied maths, Could you help me with the following?
Given ln x=7.1; ln y=8.2, Find ln(x3y7)
Given ln x=7.1: ln y=8.2, Find ln(x3/lnx7)
Thanks, Jo


Hi Jo,

The solutions to these problems rely on three properties of the logarithm function. These are

ln(a b) = ln(a) + ln(b)
ln(a/b) = ln(a) - ln(b) and
ln(ab) = b ln(a)

For your problem

ln(x3 y7)

if you apply the first of the properties above you get

ln(x3 y7) = ln(x3) + ln(y7)

and then the third of the properties gives

ln(x3 y7) = ln(x3) + ln(y7) = 3 ln(x) + 7 ln(y)

ln x = 7.1 and ln y = 8.2 so the exprression is finally

ln(x3 y7) = ln(x3) + ln(y7) = 3 ln(x) + 7 ln(y) = 3 7.1 + 7 8.2

Are you sure that your second problem is correct?



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