Solve for x in log(8x+2)+3log1=1+log(−4x+5).

The equation is: log(8x+2) + 3log1 = 1 + log(-4x+5)

Step 1: Simplify the equation Since log1 is always 0, the equation simplifies to: log(8x+2) = 1 + log(-4x+5)

Step 2: Move the constant on the left side to the right side log(8x+2) - 1 = log(-4x+5) This can be rewritten as: log(8x+2) = log(10) + log(-4x+5) Since log(10) is 1, the equation simplifies to: log(8x+2) = 1 + log(-4x+5)

Step 3: Use the property of logarithms to combine the logs on the right side log(8x+2) = log(10(-4x+5))

Step 4: Use the property of logarithms that if logb(a) = logb(c), then a = c So, 8x+2 = 10(-4x+5)

Step 5: Solve for x Expand the right side: 8x + 2 = -40x + 50 Combine like terms: 48x = 48 Divide by 48: x = 1

So, the solution to the equation log(8x+2) + 3log1 = 1 + log(-4x+5) is x = 1.