Question

solve the following equation.\\(\log_6 x = 3\\)\
rewrite the given equation without logarithms. do not solve for x.\
(type your answer using exponential notation.)\
the solution set is \\(\\{\\}\\).\
(simplify your answer.)

Explanation:

Step1: Recall logarithm definition

The logarithmic equation $\log_{b}a = c$ is equivalent to the exponential equation $b^{c}=a$ (by the definition of logarithms, where $b>0,b
eq1$).
Here, $b = 6$, $c = 3$, and $a=x$. So we rewrite $\log_{6}x = 3$ using the definition.

Step2: Rewrite the equation

Applying the definition, we get $6^{3}=x$.

Step3: Solve for the solution set

Calculate $6^{3}=6\times6\times6 = 216$. So the solution set is $\{216\}$.

Answer:

• Rewrite without logarithms: $6^{3}=x$
• Solution set: $\{216\}$