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
A mixture contains sugar solution and colored water in the ratio 5 : 8. If 22 liters of colored water is added to the mixture, the ratio becomes 3 : 7. Find the initial quantity of sugar solution in the given mixture (in liters).
The initial ratio is 5 : 8.
Let ‘k’ be the common ratio.
=> Initial quantity of sugar solution = 5 k
=> Initial quantity of colored water = 8 k
=> Final quantity of sugar solution = 5 k
=> Final quantity of colored water = 8 k + 22
Final ratio = 5 k : 8 k + 22 = 3 : 7
=> k = 6
Therefore, initial quantity of sugar solution in the given mixture (in liters) = 5 k = 30 liter
There are two buildings P and Q. If 35 persons are sent from P to Q, then the number of persons in each building is the same. If 60 persons are sent from Q to P, then the number of persons in P is double the number of persons in Q. How many persons are there in building P?