Write the exact answer using base-10 logarithms.

Question

9^-4x=4^x+10

Answer 1

9^-4x = 4^x+10

 

Take log of both sides.

 

-4x log9 = (x + 10)log4

 

x(-4 log9 - log4) = 10 log4

 

x = 10 log4 / (-4 log9 - log4)

 

You can simplify it further from here.