The equation to be solved is: log(4x+16) - log100 = log16 - 2log2

Use the relations: log a - log b = log(a/b), log + log b = log a*b and n*log a = log a^n

log(4x+16) - log100 = log16 - 2log2

=> log(4x+16) = log100 + log16 - log 2^2

=> log(4x+16) = log 100 + log 16 - log 4

=> log(4x+16) = log 100*16/4

=> log(4x+16) = log 400

We can equate 4x + 16 = 400

=> x + 4 = 100

=> x = 96

**The required value is x = 96**