Question

solve the equation. log₂8 + log₂x = 0 select the correct choice below and fill in any answer boxes present in your choice. a. x = (simplify your answer, including any radicals. use integers or fractions for any numbers in the expression. use a comma) b. there is no solution.

Explanation:

Step1: Evaluate $\log_2 8$

Since $2^3 = 8$, then $\log_2 8=3$. The equation becomes $3+\log_2 x = 0$.

Step2: Isolate $\log_2 x$

Subtract 3 from both sides: $\log_2 x=- 3$.

Step3: Convert to exponential form

By the definition of logarithms, if $\log_a b = c$, then $b=a^c$. So, $x = 2^{-3}$.

Step4: Calculate the value of $x$

$2^{-3}=\frac{1}{2^3}=\frac{1}{8}$.

Answer:

A. $x=\frac{1}{8}$