Question

let S =log(√7+√5) base 2 then find the value of log(√7-√5) base 2 with respect to S​

Answer 1

Answer:

Step-by-step explanation:

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Answer 2

Given :   log₂(√7  + √5)   =  S

To find :  log₂(√7  - √5   )

Solution:

log₂(√7  + √5)   =  S

√7  - √5  

= √7  - √5      * (√7  + √5) / (√7  + √5)

= (7 - 5) /(√7  + √5)

= 2/(√7  + √5)

log₂(√7  - √5   )  =  log₂(2/(√7  + √5))

using log (a/b) = log a - log b

= log₂ 2  - log₂ (√7  + √5)

using logₐa = 1   &  log₂ (√7  + √5) = S

= 1  -  S

log₂(√7  - √5   ) = 1 - log₂(√7  + √5)

log₂(√7  - √5   )  = 1  -  S

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