Question

1. solve for x in the logarithmic equation \\(\log_{\sqrt{3}} x - 8 = 0\\).\

\\(\bigcirc\\) \\(x = 9.45\\)\
\\(\bigcirc\\) \\(x = 1\\)\
\\(\bigcirc\\) \\(x = 81\\)\
\\(\bigcirc\\) \\(x = 1.32\\)

Explanation:

Step1: Isolate the logarithm term

$\log_{\sqrt{3}} x = 8$

Step2: Convert to exponential form

$x = (\sqrt{3})^8$

Step3: Simplify the exponential expression

First, rewrite $\sqrt{3}$ as $3^{\frac{1}{2}}$, so $x = (3^{\frac{1}{2}})^8 = 3^{\frac{1}{2} \times 8} = 3^4 = 81$

Answer:

$x = 81$