(a) If $$ \log _{x} 9=2 $$, then $$ x=\square $$ (b) If $$ \log _{x} 256=4 $$, then $$ x=\square $$ Question Help: $$ \square $$ Video

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Solve the quadratic equation by following steps:
- step0: Solve using square roots:
  $$x^{2}=9$$
- step1: Simplify the expression:
  $$x=\pm \sqrt{9}$$
- step2: Simplify the expression:
  $$x=\pm 3$$
- step3: Separate into possible cases:
  $$\begin{align}&x=3\&x=-3\end{align}$$
- step4: Rewrite:
  $$x_{1}=-3,x_{2}=3$$
Solve the equation $$ x^{4}=256 $$.
Solve the equation by following steps:
- step0: Solve for $$x$$:
  $$x^{4}=256$$
- step1: Simplify the expression:
  $$x=\pm \sqrt[4]{256}$$
- step2: Simplify:
  $$x=\pm 4$$
- step3: Separate into possible cases:
  $$\begin{align}&x=4\&x=-4\end{align}$$
- step4: Rewrite:
  $$x_{1}=-4,x_{2}=4$$
Let's solve each part step by step.

### Part (a)
Given the equation:
$$
\log_{x} 9 = 2
$$
This can be rewritten in exponential form:
$$
x^{2} = 9
$$
Now, we solve for $$ x $$:
$$
x = \pm 3
$$
However, since the base of a logarithm must be positive and not equal to 1, we take the positive solution:
$$
x = 3
$$

### Part (b)
Given the equation:
$$
\log_{x} 256 = 4
$$
This can also be rewritten in exponential form:
$$
x^{4} = 256
$$
Now, we solve for $$ x $$:
$$
x = \pm 4
$$
Again, we only consider the positive solution:
$$
x = 4
$$

### Final Answers
(a) $$ x = 3 $$

(b) $$ x = 4 $$
$$ x = 3 $$ for part (a) and $$ x = 4 $$ for part (b).

(a) If , then
(b) If , then
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