Question

What is the solution to log base 2 of (2×3-8) divided by log base 2 of x equals log base 2 of x?

A) x = 1
B) x = 2
C) x = 3
D) x = 4

Answer 1

The equation log base 2 of (2×3-8) divided by log base 2 of x equals log base 2 of x has no solution since log base 2 of -2 does not exist. Choices A, B, C, and D do not provide the correct solution.

Step-by-step explanation:

The solution to the given logarithmic equation log base 2 of (2×3-8) divided by log base 2 of x equals log base 2 of x can be found by applying logarithmic properties. Given the property that the logarithm of a division is the difference of the logarithms, the equation can be rewritten as follows:

log2(2×3 - 8) - log2(x) = log2(x)

By simplifying and solving for x, we arrive at:
log2((2×3) - 8) = 2log2(x)

log2(6 - 8) = 2log2(x)

log2(-2) does not exist since the logarithm of a negative number is undefined, meaning that the original equation has no solution. However, the possible choices provided suggest a misinterpretation or error in the formulation of the equation. Therefore, none of the options A) x = 1, B) x = 2, C) x = 3, or D) x = 4 is the correct solution to the given equation.