Logarithms

Question

If k=log2 ( √9 + √5), express log_√2 (√9 - √5) in terms of k.

Ans: 2(2-k) 

Answer 1

 

 2^K = √9 + √5

 

√2^{p  = √9 - √5} 

 

 Multiply both sides:

2 ^{1/2 P + k} = 4 =2^2

 

1/2 P + k = 2

 

  P = 4 - 2K

 

 P = 2 ( 2-k)

 

  4 - 2k = log_{√2 ( 3 -} √5 )