Solve for x in log(5x+7)+4log5=4+log(x−3).x=−5x=6x=5x=−14

The question seems to be a bit jumbled, but I'll try to solve the initial logarithmic equation you provided: log(5x+7) + 4log5 = 4 + log(x-3).

Step 1: Simplify the equation by using the properties of logarithms.

log(5x+7) + log(5^4) = 4 + log(x-3)

Step 2: Simplify further by converting the log of 5^4 to a number.

log(5x+7) + log(625) = 4 + log(x-3)

Step 3: Combine the logs on the left side of the equation.

log[(5x+7)*625] = 4 + log(x-3)

Step 4: Simplify the left side of the equation.

log[3125x + 4375] = 4 + log(x-3)

Step 5: Subtract log(x-3) from both sides of the equation.

log[3125x + 4375] - log(x-3) = 4

Step 6: Use the quotient rule of logarithms to simplify the left side of the equation.

log[(3125x + 4375)/(x-3)] = 4

Step 7: Convert the equation from logarithmic form to exponential form.

(3125x + 4375)/(x-3) = 10^4

Step 8: Solve for x.

Unfortunately, this equation does not have a simple solution for x. You would need to use numerical methods to find an approximate solution.

As for the other equations you provided (x=−5, x=6, x=5, x=−14), they are not related to the initial logarithmic equation.