Solve the equations. Log(6x-1) = Log(x+1) + log4
To solve the equation Log(6x-1) = Log(x+1) + log4, we'll use logarithmic properties and algebraic techniques to simplify and solve for x.
Step 1: Apply the logarithmic property
Log(6x-1) = Log[(x+1) * 4]
Step 2: Apply the property of logarithm multiplication
Log(6x-1) = Log(4x + 4)
Step 3: Apply the property of logarithm equality
6x - 1 = 4x + 4
Step 4: Solve for x
6x - 4x = 4 + 1
2x = 5
x = 5/2
x = 2.5
Therefore, the solution to the equation Log(6x-1) = Log(x+1) + log4 is x = 2.5.