Question

Which of the following is true regarding the solutions to the logarithmic equation below?

2 log Subscript 3 Baseline (x) = 4. log Subscript 3 Baseline (x squared) = 4. x squared = 3 Superscript 4. x squared = 81. x = 9, negative 9

Answer 1

To solve the logarithmic equation 2 log3(x) = 4, we use the property that the logarithm of a number raised to an exponent is the product of that exponent and the logarithm of the number, which simplifies to x^2 = 81 and then to the solutions x = 9 and x = -9. However, x must be positive, so the only valid solution is x = 9.

Step-by-step explanation:

To solve the logarithmic equation 2 log3(x) = 4, we apply the properties of logarithms. One key property is that the logarithm of a number raised to an exponent is the product of the exponent and the logarithm of the number. Using this property, we can rewrite log3(x2) as 2 log3(x), which matches the left-hand side of the equation, indicating that both sides are equal.

Upon equating 2 log3(x) with 4, we divide both sides by 2 to isolate the logarithm:

log3(x) = 2.

Now, by rewriting the logarithmic equation in exponential form, we have:

x = 32,

which simplifies to:

x2 = 81.

Finally, we take the square root of both sides to find the possible solutions for x:

x = 9, x = -9.

However, because x represents the argument of a logarithm, it must be positive. Therefore, the only valid solution to the original equation is:

x = 9.

Answer 2

D.

Step-by-step explanation:

x=9 is a true solution and x = -9 is an extraneous solution

Answer on Edgen. 2020