Question

If a^(2x + 2) = 1, a is not equal to 1, then x is equal to​

Answer 1

Answer:

a

2x+2

=1

⇒a

2x+2

=a

0

⇒2x+2=0

⇒x=−1

Answer 2

Step-by-step explanation:

Given :-

a^(2x + 2) = 1, a ≠ 1

To find :-

Find the value of x ?

Solution :-

Method -1:-

Given that

a^(2x + 2) = 1

On writing it as logarithmic form

=> log 1 to the base a = 2x+2

=> 0 = 2x+2

=> 2x+2 = 0

=> 2x = -2

=> x = -2/2

=> x = -1

Therefore, x = -1

Method -2:-

a^(2x + 2) = 1

On taking Logarithms both sides then

=> log a^(2x + 2) = log 1

=> (2x+2) log a = log 1

Since , log a^m = m log a

=> (2x+2) log a = 0

Since , log 1 = 0

=> 2x log a + 2 log a = p

=> 2x log a = -2 log a

=> x log a = - log a

=> x = - log a / log a

=> x = -1

Therefore, x = -1

Answer :-

The value of x for the given problem is -1

Check:-

If x = -1 then LHS of the given equation is

a^(2×-1+2)

=> a^(-2+2)

=> a^(0)

=> 1

=> RHS

=> LHS = RHS is true for x = -1

Used formulae :-

→ a^x = N => log N to the base a = x

→ log a^m = m log a

→ log 1 = 0

→ a^0 = 1