Question

solve the exponent of the equation.

(√6)^x-2=1

Answer 1

Given : ( √6 )^[ x - 2 ] = 1

From the identities of indices, we know that any number having 0 in its power is directly equal to 1.

Therefore, writing 1 as ( √6 )^0.

$\implies ( \sqrt{6} )^{ x-2} = (\sqrt{6})^0$

From the identities of indices, we know that when bases are equal ( with some power on them ), power are also equal.

∴ x - 2 = 0

⇒ x - 2 + 2 = 0 + 2

⇒ x = 2

Hence, the value of x is 2.