Question

Solve the equation log2(2x) = log216 using the one-to-one property of logarithms.

Answer 1

By applying the one-to-one property of logarithms, since both have a base of 2, the arguments are set equal to each other, yielding 2x = 16. Dividing both sides by 2, we find that x equals 8.

Step-by-step explanation:

To solve the equation log2(2x) = log2(16) using the one-to-one property of logarithms, we can set the arguments of the logarithms equal to each other because the bases are the same.

Here is the step-by-step explanation:

1. Since the bases of the logarithms are equal (both are base 2), we know that the arguments must also be equal. This gives us 2x = 16.
2. To find the value of x, we divide both sides of the equation by 2 which simplifies to x = 8.

Therefore, the solution to the equation log2(2x) = log2(16) is x = 8.