Question

3(log9 x)2 = 6 log9 x
a. True
b. False

Answer 1

The statement 3(log9 x)2 = 6 log9 x is true because, after simplifying the equation according to the properties of logarithms, we find that both sides are equal, yielding a true statement.

Step-by-step explanation:

The student is asking whether the statement 3(log9 x)2 = 6 log9 x is true or false. This involves understanding the properties of logarithms. A key property that can be used here is that the logarithm of a number raised to an exponent is the product of the exponent and the logarithm of the number (in algebraic form, loga(bc) = c loga(b)). Therefore, we can simplify the equation by dividing both sides by log9 x, given that log9 x is not equal to zero.

1. 3(log9 x)^2 equals 3 * (log9 x) * (log9 x)
2. Divide both sides by log9 x: 3 * (log9 x) = 6
3. This simplifies to log9 x = 2, after dividing both sides by 3
4. The initial equation then can be written as: 6 = 6, which is true

Therefore, the answer is A. True.