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Here is one way that doesn't use  logs

 

8^5x  =  (2^3)^5x   =   2^15x

 

16^*(3x+4) = (2^4)^(3x+4) = 2^(12x+16)

 

now equate the exponents

 

15x   = 12x + 16

3x = 16

x = 16/3