Question

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

Answer 1

Answer:

$x =\pm \sqrt{26}$

Step-by-step 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 ,

$\implies 1 = x^2 - 25 \\\\\implies x^2 = 25 + 1 \\\\\implies x^2 = 26 \\\\\implies x =\sqrt{26} \\\\\implies x = \pm \sqrt{ 26}$

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