Final answer:
To solve the equation log¹⁶x = ⅓, we convert the log equation to an exponential one, indicating that 16 to the power of 1/2 equals x. Calculating the square root of 16 gives us the value x = 4.
Step-by-step explanation:
To solve the equation log¹⁶x = ⅓, we need to understand that the logarithm function and the exponential function are inverse operations. The logarithm of a number is the power to which the base must be raised to obtain that number. When we have log base 16 of x equals 1/2, it means that 16 raised to the power of 1/2 must equal x. We can express 1/2 as an exponent in the form of a square root. Therefore, x can be found by calculating the square root of 16, which equals 4.
Solution Steps
Express the logarithmic equation in exponential form: 16^(1/2) = x.
Calculate the value of 16^(1/2), which is the square root of 16.
Determine that the square root of 16 equals 4, so x = 4.
Since the base of the logarithm is 16 and the equation has a log result of 1/2, the value of x is simply the square root of 16, which is 4.