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Find the constant k so that

 


for all positive real numbers x and y with y ≠ 1.

 Mar 31, 2020
 #1
avatar+112419 
+1

We  can write

 

log y^5 (x^3)  = log y (x^k)

 

Using  the change of base  theorem  we can  write

 

log x^3                log x^k          

_______   =     ________     simplify

log y^5                 log y

 

 

3 log  x            k log x

______  =    ________

5 log y              log y

 

(3/5) log (x) / log (y)   =  (k) log (x) / log (y)

 

So

 

(3/5)   = k

 

 

cool cool cool

 Mar 31, 2020

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