Logbase3(4X +1) -Logbase3(3X -5) =2

Answer 1

Let's solve this logarithmic equation step by step.

Using the logarithmic properties:
1. Logbase3(4X + 1) - Logbase3(3X - 5) = Logbase3((4X + 1)/(3X - 5))

Rearranging the equation:
2 = Logbase3((4X + 1)/(3X - 5))

Now, we can rewrite the equation in exponential form:
3^2 = (4X + 1)/(3X - 5)

9 = (4X + 1)/(3X - 5)

Cross-multiplying:
9(3X - 5) = 4X + 1

27X - 45 = 4X + 1

Subtracting 4X from both sides:
27X - 4X - 45 = 1

Simplifying the equation:
23X - 45 = 1

Adding 45 to both sides:
23X = 46

Dividing both sides by 23:
X = 2

Therefore, the solution to the equation is X = 2.