Question

solve the given exponential equation 2 to the power 2 X + 1 equal to 4 to the power 2x - 1​

Answer 1

Answer:

x = 3/2

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Step-by-step explanation:

Answer 2

The value of x is 3/2

GIVEN

Mathematical expression;

2²ˣ⁺¹ = 4²ˣ⁻¹

TO FIND

The value of x

SOLUTION

We can simply solve the above problem as follows;

It is given,

2²ˣ⁺¹ = 4²ˣ⁻¹

Simplifying the RHS

We can write the base 4 as 2²

Therefore,

4²ˣ⁻¹ = (2²)²ˣ⁻¹

Applying the formula,

(aⁿ)ᵐ = aⁿˣm

Therefore;

(2²)²ˣ⁻¹ = 2⁴ˣ⁻²

Now comparing LHS and RHS

2²ˣ⁺¹ = 2⁴ˣ⁻²

We can observe that the base in LHS and RHS is same.

Equating the exponents;

2x+1 = 4x-2

1 + 2 = 4x-2x

3 = 2x

x = 3/2

Hence, The value of x is 3/2

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