Question

If log4 + log(13x+1) = log(5x+9) + 1, then what is the value of x?

Note: Assume all log represented is to the base of 10.

Answer 1

Thanks for the puzzle.

log4 + log(13x+1) = log(5x+9) + 1
=> log4 + log(13x + 1) = log(5x + 9) + log10 ..... [since 1 = log 10]
=> log (52x + 4) = log (50x + 90)
=> 52x + 4 = 50x + 90
=> x = 43

Therefore, x = 43.