How to solve log8/log2? working out too plz?
2017-02-24 7:36 pm
log8/log2 when i type in my calculator its 3 but 8/2 is equal to 4. So then its log 4 but how does it equal 3? Please show working, thanks
回答 (5)
2017-02-24 7:41 pm
✔ 最佳答案
Identity used: log(aⁿ) = n log(a)
log(8) / log(2)
= log(2³) / log(2)
= 3 log(2) / log(2)
= 3
[Note that log(8)/log(2) ≠ log(8/2)]
2017-02-24 8:51 pm
= Log(8) / Log(2) → you know that: 8 = 2 * 2 * 2 = 2^3
= Log(2^3) / Log(2) → you know that: Log(x^a) = a.Log(x)
= 3.Log(2) / Log(2) → you can simplify by Log(2)
= 3
= Log(2^3) / Log(2) → you know that: Log(x^a) = a.Log(x)
= 3.Log(2) / Log(2) → you can simplify by Log(2)
= 3
2017-02-24 8:16 pm
log(a) / log(b) is not a/b. If it was that easy, why would we use logarithms?
log(8) / log(2) =>
log(2^3) / log(2) =>
3 * log(2) / log(2)
The entire expression of log(t)/log(t) cancels out
3 * 1 =>
3
log(8) / log(2) =>
log(2^3) / log(2) =>
3 * log(2) / log(2)
The entire expression of log(t)/log(t) cancels out
3 * 1 =>
3
2017-02-24 8:00 pm
Remember 8 = 2 x 2 x 2 = 2^3
Hence
log8 = log2^3
log2^3 = 3log2 (The rules for indices and logarithms).
Hence
log 8 / log2 = 3log2/log2
Cancel down by 'log2'
Hence answer is '3' .
Hence
log8 = log2^3
log2^3 = 3log2 (The rules for indices and logarithms).
Hence
log 8 / log2 = 3log2/log2
Cancel down by 'log2'
Hence answer is '3' .
2017-02-24 7:43 pm
8 is 2^3 so by the rules of logs
log(8) = log[2^3} = 3log(2), and so,
log(8)/log(2) = 3
Extra note: A logarithm is a power.
For example when you write log(1000) = 3
that 3 is the power in 10^3 = 1000
The ratio of log(8) to log(2) is NOT the same as the ratio 8 to 2
As we have shown log(8)/log(2) = 3, whereas 8/2 = 4
Powers and simple division are different things
log(8) = log[2^3} = 3log(2), and so,
log(8)/log(2) = 3
Extra note: A logarithm is a power.
For example when you write log(1000) = 3
that 3 is the power in 10^3 = 1000
The ratio of log(8) to log(2) is NOT the same as the ratio 8 to 2
As we have shown log(8)/log(2) = 3, whereas 8/2 = 4
Powers and simple division are different things
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