Answer:
Explanation:
To express 7 in terms of X, we can use the equation given: log Y + 2 log X = 10.
Let's start by isolating the term with the log Y. We can do this by subtracting 2 log X from both sides of the equation:
log Y = 10 - 2 log X.
Next, we can use the properties of logarithms to simplify the equation further. Specifically, we can use the power rule of logarithms, which states that log a^b = b log a. Applying this rule, we can rewrite the equation as:
log Y = log (10 / X^2).
Now, we can remove the logarithm by raising both sides of the equation to the base 10:
10^(log Y) = 10^(log (10 / X^2)).
Since 10 raised to the power of log base 10 is equal to the argument inside the logarithm, we have:
Y = 10 / X^2.
Finally, to express 7 in terms of X, we substitute Y with 7 in the equation:
7 = 10 / X^2.
Now, we can solve for X. Multiplying both sides of the equation by X^2 gives us:
7X^2 = 10.
Dividing both sides by 7 gives us:
X^2 = 10/7.
Taking the square root of both sides gives us two possible solutions:
X = sqrt(10/7) or X = -sqrt(10/7).
Therefore, 7 can be expressed in terms of X as either sqrt(10/7) or -sqrt(10/7).