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avatar+394 

Find the constant k so that \(\log_{y^5}(x^3) = k \cdot\log_y(x)\) for all positive real numbers x and y with \(y \neq 1. \)

 

I'm unsure how to start this off. I tried turning it into exponential form but it made no sense. I think I might have to try the Change of Base formula. Can someone start me off?

 Mar 19, 2021
 #1
avatar+121003 
+1

Note   k *  log y x  can be written as   log y x^k

 

Using  the  change-of-base  we  have  that

 

log x^3  /  log y^5    =   log x^k    / log y       and we can write

 

3 * log x  / 5* log y  =  k * log x  / log y        multiply both sides  by  log y  /log x    and we get that

 

3  /  5   =   k

 

 

cool cool cool

 Mar 19, 2021
 #2
avatar+394 
+1

Thx CPhill

 Mar 19, 2021

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