Question

x^((x+2)(x+3) =1 how can I solve ?

Answer 1

Given equation is x^[ ( x + 2 )( x + 3 ) ] = 1, although the equation doesn't have x( as base ) on both sides, it can be solved by using an identity from exponents.

Here, we won't use that identity directly.


Given,

= > x^[ ( x + 2 )( x + 3 ) ] = 1


We know that 1 can be written as a / a, where a can be any number.

In this condition, we have to write 1 as x / x.


= > x^[ ( x + 2 )( x + 3 ) ] = x / x


From the properties, we know

a^n / a^m = a^( n - m )

= > x^[ ( x + 2 )( x + 3 ) ] = x^( 1 - 1 )

= > x^[ ( x + 2 )( x + 3 ) ] = x^0


Since values of both the sides are equal, with same base, powers should be equal.

= > ( x + 2 )( x + 3 ) = 0

= > x + 2 = 0 Or x + 3 = 0

= > x = - 2 Or x = - 3


Hence the required numeric value of x is either - 2 or - 3.

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