Question

Solve 16¹−ˣ=32³ˣ ⁵ exponential equation.

a) x= −1/4
b) x= −1/2
c) x= 1/4
d) x= 1/2

Answer 1

To solve the exponential equation 16¹ − ˣ = 32³ ˣ ⁵, we can simplify the equation by expressing 16 and 32 as powers of 2. The equation can be further simplified by equating the exponents and solving for x, which gives x = -1/2. Therefore, the answer is (b) x = -1/2.

Step-by-step explanation:

To solve the exponential equation 16¹−ˣ=32³ˣ⁵, we can start by writing both sides with the same base. This can be done by expressing 16 and 32 as powers of 2: 16 = 2⁴ and 32 = 2⁵.

Substituting these values, we have (2⁴)¹−ˣ = (2⁵)³ˣ⁵. Now, using the property of exponents that says (aⁿ)ᵐ = aⁿᵐ, we can simplify the equation to 2⁴−4ˣ = 2ⁱ⁵ˣ⁵.

Next, we can equate the exponents: 4 - 4x = 15x - 25. Solving for x, we get x = -1/2. Therefore, the correct answer is (b) x = -1/2.