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# C2 Log Question watch

1. This one stumped me when I was helping a friend.

Find the values for which log3(x) - 2logx(3) = 1

They give the answers as 1/3 and 9.

I am mildly confused.

2. (Original post by NikolaiJ)
This one stumped me when I was helping a friend.

Find the values for which log3(x) - 2logx(3) = 1

They give the answers as 1/3 and 9.

I am mildly confused.

log3(x) - 2logx(3) = 1
log3(x) - logx(3²) = 1
log3(x) - logx(9) = 1
log3(x) - log3(9)/log3(x) = 1

Let log3(x) = y

y - 2/y = 1
y² - 2 = y
y² - y - 2 = 0
(y-2)(y+1) = 0

y = 2 or y = -1
=> log3(x) = 2 or log3(x) = -1
x = 3² or x = 3-1
x = 9 or x = 1/3

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