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p6aig1alittdellick p6aig1alittdellick
  • 21-11-2016
  • Mathematics
Answered

Write log8 3 as a logarithm of base 5.


1) (log3)5/(log8)5

2) (log5)3/(log5)8

3) (log8)5/(log3)5

4) (log5)8/(log5)3 ...?

Verified Answer :

JcAlmighty
JcAlmighty JcAlmighty
  • 22-11-2016

The answer is 2) (log5)3/(log5)8

We will use the change-of-base formula: \(log_a(x)= \frac{log_b(x)}{log_b(a)}\)

So, if we want to write log8 3 as a logarithm of base 5,  in these example a = 8, x = 3, b = 5:
\(log_8(3)= \frac{log_5(3)}{log_5(8)}\)

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