Question

Log3(5x+3)=log3(7x+3)

Answer 1

Решение во вложении.

Answer 2

To solve the equation log3(5x+3) = log3(7x+3), we can use the properties of logarithms. The basic property we'll use is that if log3(a) = log3(b), then a = b.

Step 1: Set the arguments of the logarithms equal to each other:

5x + 3 = 7x + 3

Step 2: Simplify the equation by moving the variables to one side and the constants to the other side:

5x - 7x = 3 - 3

-2x = 0

Step 3: Solve for x:

x = 0

So the solution to the equation is x = 0. However, we should check if this solution is valid, as the domain of the logarithmic function requires its argument to be greater than 0.

Step 4: Check the validity of the solution:

For x = 0, both arguments of the logarithms become:

log3(5(0) + 3) = log3(3) = log3(7(0) + 3) = log3(3)

Since the argument of the logarithm is the same for both sides of the equation, x = 0 is a valid solution.

Therefore, the only solution to the equation log3(5x+3) = log3(7x+3) is x = 0.