Question

solve the equation.
log₂ 4 - log₂ x = 2

select the correct choice below and fill in any answer boxes present in your choice.
a. x = 64 (simplify your answer, including any radicals. use integers or fractions for any numbers in the)
b. there is no solution.

Explanation:

Step1: Simplify $\log_2 4$

Since $2^2 = 4$, then $\log_2 4=2$. The equation becomes $2-\log_2 x = 2$.

Step2: Isolate $\log_2 x$

Subtract 2 from both sides: $-\log_2 x=2 - 2$, so $-\log_2 x = 0$, then $\log_2 x=0$.

Step3: Solve for $x$

By the definition of logarithms, if $\log_2 x = 0$, then $x = 2^0=1$.

Answer:

The answer in the correct - choice format: B. There is no solution (the given choice A with $x = 64$ is incorrect, the correct value of $x$ is 1 which is not among the given choices).