Question

Solve the following logarithmic equation:
log(5)(3x-7)= log(5)(x-1)

Answer 1

The logarithmic equation log_5(3x-7) = log_5(x-1) is solved by equating the arguments of the logarithms to get 3x - 7 = x - 1. Simplifying this leads to the solution x = 3.

Step-by-step explanation:

To solve the given logarithmic equation log5(3x-7) = log5(x-1), we use the property of logarithms that states if loga(b) = loga(c), then b = c. This property allows us to equate the arguments of the logarithms when the bases are the same.

Applying this property, we have 3x - 7 = x - 1. To solve for x, we simplify the equation:

1. Move the x terms to one side by subtracting x from both sides: 3x - x = 7 - 1
2. Simplify the resulting equation: 2x = 6
3. Divide both sides by 2 to find x: x = 3

Therefore, the solution to the logarithmic equation is x = 3.