Determine logarithm versus known values of a,b We know log_(30)(3)=a, log_(30)(5)=b. How to determine log_(30)(16)?

bergvolk0k

bergvolk0k

Answered question

2022-10-20

Determine logarithm versus known values of a , b
We know log 30 ( 3 ) = a , log 30 ( 5 ) = b . How to determine log 30 ( 16 )?

Answer & Explanation

Audrey Russell

Audrey Russell

Beginner2022-10-21Added 16 answers

For convenience we'll denote l o g 30 by l o g
We note that
1 = l o g ( 30 ) = l o g ( 6 × 5 ) = l o g ( 6 ) + l o g ( 5 ) = l o g ( 6 ) + b l o g ( 6 ) = 1 b
But then we have
1 b = l o g ( 6 ) = l o g ( 2 × 3 ) = l o g ( 2 ) + l o g ( 3 ) = l o g ( 2 ) + a l o g ( 2 ) = 1 b a
Can you finish from here?

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