M4maths Previous Puzzles

19 Sep 2019 Logarithm

If log2 + log(3x+1) = log(2x-9) + 2, then value of x is ?
Note: Assume all log represented above is to the base of 10.

OPtion

1) 441/94
2) 451/94
3) 461/94
4) 441/97
5) 461/97
6) 451/97
7) 431/97
8) 451/91
9) 451/93
10)None of these

Solution

Considering base is 10, so 1 could be represented as Log10
=> log2 + log(3x+1) = log(2x-9) + log100

Let’s revise the formula for Logs
Log(XY) = LogX+LogY
Applying the formula we get:
Log[2*(3x+1)] = Log[100*(2x-9)]
Solving
=> 6x + 2 = 200x - 900
=> 194x= 902
=> x = 451/97

Correct Option: 6 Best Solution (1)