Question

8ˣ⁴=16²ˣ logarithmic function
a) x = -2
b) x = -1/2
c) x = 1/2
d) x = 2

Answer 1

To solve the equation 8ˣ⁴ = 16²ˣ, take the natural logarithm of both sides and use the property of logarithms to simplify. The correct answer is c) x = 1/2.

Step-by-step explanation:

To solve the equation 8ˣ⁴ = 16²ˣ, we can take the natural logarithm of both sides. The natural logarithm cancels out the exponential function. By using the property of logarithms that log(a) - log(b) = log(a/b), we can simplify the equation to 4ln(8) = 2xln(16). Dividing both sides by 2ln(16), we get x = 2ln(8) / ln(16).

Using the change of base formula, we can convert the natural logarithms to base 10 logarithms: x = 2log(8) / log(16). Evaluating the logarithms, we find that x = 2/3. Therefore, the correct answer is c) x = 1/2.