How to answer with using log? 4^(10-2x)=4096

Question

anybody know how to do solve this? please thank you

Answer 1

Arturo's solution using logarithms is correct.  Another way to solve the problem without logarithms is to express both sides of the equation as powers of the same base:

 

    4^10-2x  = 4096

 

   (2²)^10-2x = 2¹²

 

    2^20-4x = 2¹²

 

    So, 20-4x = 12

 

             -4x = -8

 

                x = 2

 

Answer 2

4^{10 - 2x} = 4096

 

Take log on both sides, and apply the properties of logs.

 

(10 - 2x) log4 = log4096

 

10 - 2x = log4096 / log4

 

2x = 10 - (log4096 / log4)

 

x = (1/2)[10 - (log4096 / log4)] = ?

 

(true for any base)