Final answer:
To find the value of x given that log289=2, we recognize that 289 must be equal to 10 raised to the power of 2, but since 10 squared is 100, not 289, we realize the correct relationship should be 289 = x^2. Solving for x, we take the square root of 289, which yields x = 17.
Step-by-step explanation:
The question asks us to find the value of x given that log289=2. This is a logarithmic equation where the logarithm is given with the base 10 by default. To solve for x, we need to recognize that the logarithm of a number is the power to which the base must be raised to produce that number. In this case, the number 289 is equal to 10 raised to the power of 2 since log(289) = 2. Therefore, we must find the number x such that 102 equals 289. However, we know that 102 is 100, which is not equal to 289, indicating a mistake in the initial assumption. Instead, we should consider the actual relationship 289 = x2 and solve for x by taking the square root of 289, which is 17. Thus, x must equal 17.