p6aig1alittdellick p6aig1alittdellick
  • 21-11-2016
  • Mathematics
contestada

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 ...?

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JcAlmighty
JcAlmighty JcAlmighty
  • 22-11-2016
The answer is 2) (log5)3/(log5)8

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

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