Question

What are the potential solutions of In(x^2-25)=0?

Answer 1

C

Explanation:

Answer 2

`x =\pm √(26)`

Explanation:

Given :-

• ln ( x² - 25 ) = 0

And we need to find the potential solutions of it. The given equation is the logarithm of x² - 25 to the base e . e is Euler's Number here. So it can be written as ,

Equation :-

`\implies log_e {(x^2-25)}= 0`

In general :-

• If we have a logarithmic equation as ,

`\implies log_a b = c`

Then this can be written as ,

`\implies a^c = b`

In a similar way we can write the given equation as ,

`\implies e^0 = x^2 - 25`

• Now also we know that
  `a^0 = 1` Therefore , the equation becomes ,

`\implies 1 = x^2 - 25 \\\\\implies x^2 = 25 + 1 \\\\\implies x^2 = 26 \\\\\implies x =√(26) \\\\\implies x = \pm √( 26)`

Hence the Solution of the given equation is ±√26.