Question

find the value of x.
\\(\log_3 x = 4\\)
\\(\bigcirc\\) a. \\(7\\)
\\(\bigcirc\\) b. \\(12\\)
\\(\bigcirc\\) c. \\(27\\)
\\(\bigcirc\\) d. \\(81\\)

Explanation:

Step1: Recall the logarithm definition

The logarithmic equation $\log_{b}a = c$ is equivalent to the exponential equation $b^{c}=a$.

Step2: Apply the definition to the given equation

For the equation $\log_{3}x = 4$, using the definition of logarithms (where $b = 3$, $c = 4$, and $a = x$), we convert it to the exponential form: $3^{4}=x$.

Step3: Calculate $3^{4}$

We know that $3^{4}=3\times3\times3\times3 = 81$. So, $x = 81$.

Answer:

D. 81