Solve for Log (x -1 ) + 2 = log (3x + 2) + log 25?

To solve this equation, we will first combine the logarithms on the right side of the equation using the product rule of logarithms:

log (3x + 2) + log 25 = log ((3x + 2) * 25)
log (3x + 2) + log 25 = log (75x + 50)

Now, we can rewrite the equation as:

log (x - 1) + 2 = log (75x + 50)

Next, we will use the property of logarithms that states log a + log b = log (a * b) to combine the logarithms on the left side of the equation:

log ((x - 1) * 100) = log (75x + 50)

Now, we have:

(x - 1) * 100 = 75x + 50

Expanding the left side of the equation:

100x - 100 = 75x + 50

Subtracting 75x from both sides:

25x - 100 = 50

Adding 100 to both sides:

25x = 150

Dividing by 25:

x = 6

Therefore, the solution to the equation log (x - 1) + 2 = log (3x + 2) + log 25 is x = 6.