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# How to solve this math question?

### 4 Answers

- la consoleLv 71 month ago
= Log[x](16) / Log[x](2) → recall: Log[a](x) = Ln(x) / Ln(a) ← where a is the base

= [Ln(16) / Ln(x)] / [Ln(2) / Ln(x)]

= Ln(16) / Ln(2)

= Ln[2^(4)] / Ln(2) → you know that: Ln(x^a) = a.Ln(x)

= 4.Ln(2) / Ln(2)

= 4

- ignoramusLv 71 month ago
You usually need to know what the base of the logarithms is (that is, you need to know x).

However, in this case (which is a very particular example), since 16 = 2^4, you can say

suppose that log{x} 2 = n . . . . (can't do subscripts on here)

then log{x}16 = log{x}(2^4) = 4log{x}2

therefore log{x}16 / log{x}2 = 4log{x}2 / log{x}2 = 4

- Anonymous1 month ago
Start by reading the most basic logarithm properties.