Question

solve the equation.
log₃ 7 - log₃ x = 2
select the correct choice below and fill in any answer boxes pre
○ a. x =
(simplify your answer, including any radicals. use integer
○ b. there is no solution.

Explanation:

Step1: Use log - rule

By the quotient - rule of logarithms $\log_a M-\log_a N = \log_a\frac{M}{N}$, the equation $\log_3 7-\log_3 x = 2$ can be rewritten as $\log_3\frac{7}{x}=2$.

Step2: Convert to exponential form

The logarithmic equation $\log_a b = c$ is equivalent to the exponential equation $a^c = b$. So, $\log_3\frac{7}{x}=2$ is equivalent to $3^2=\frac{7}{x}$.

Step3: Solve for x

Since $3^2 = 9$, we have the equation $9=\frac{7}{x}$. Cross - multiply to get $9x = 7$. Then $x=\frac{7}{9}$.

Answer:

A. $x=\frac{7}{9}$