Question

Find the solution of the equation, logx−logx−1²=2log(x−1).

a) x=2
b) x=3
c) x=4
d) x=5

Answer 1

To solve the given equation, simplify by combining logs, apply properties of logarithms, and solve the resulting quadratic equation.

Step-by-step explanation:

To solve the given equation, we will use the properties of logarithms. Firstly, we can simplify the equation by combining the logs on the left side, using the property log a - log b = log(a/b). This gives us:

log(x/(x-1)²) = 2log(x-1)

Next, we can simplify further by applying the property log a^b = b * log a on the right side:

log(x/(x-1)²) = log((x-1)²)

Now, since the left side and right side of the equation have the same base, we can equate the arguments inside the logs:

x/(x-1)² = (x-1)²

Expanding and simplifying this equation will give us a quadratic equation. Solving this quadratic equation, we find that the solution is x = 4.