Question

solve the given exponential equations.
(√6) ke Power x-2=1​

Answer 1

Answer:

$\displaystyle{\boxed{\red{\sf\:x\:=\:2\:}}}$

Step-by-step-explanation:

We have to solve an exponential equation.

We have to find the value of x.

The given exponential equation is

$\displaystyle{\sf\:(\:\sqrt{6}\:)^{x\:-\:2}\:=\:1}$

Now,

$\displaystyle{\sf\:(\:\sqrt{6}\:)^{x\:-\:2}\:=\:1}$

$\displaystyle{\implies\sf\:(\:6^{\frac{1}{2}}\:)^{x\:-\:2}\:=\:1}$

$\displaystyle{\implies\sf\:6^{\frac{1}{2}\:\times\:(\:x\:-\:2\:)}\:=\:1\:\qquad\dots[\:(\:a^m\:)^n\:=\:a^{m\:n}\:]}$

$\displaystyle{\implies\sf\:6^{\frac{x\:-\:2}{2}}\:=\:1}$

$\displaystyle{\implies\sf\:6^{\frac{x\:-\:2}{2}}\:=\:6^0\:\qquad\dots[\:a^0\:=\:1\:]}$

$\displaystyle{\implies\sf\:\dfrac{x\:-\:2}{2}\:=\:0\:\qquad\dots[\:Bases\:are\:equal\:]}$

$\displaystyle{\implies\sf\:x\:-\:2\:=\:0}$

$\displaystyle{\implies\underline{\boxed{\red{\sf\:x\:=\:2\:}}}}$