Solve for x 3^x=1/( square root of 3)

$3^{x} = \frac{1}{\sqrt{3}}$

Step 1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{3}$ as $3^{\frac{1}{2}}$ .

$3^{x} = \frac{1}{3^{\frac{1}{2}}}$

Step 2

Move $3^{\frac{1}{2}}$ to the numerator using the negative exponent rule $\frac{1}{b^{n}} = b^{- n}$ .

$3^{x} = 3^{- \frac{1}{2}}$

Step 3

Since the bases are the same, then two expressions are only equal if the exponents are also equal.

$x = - \frac{1}{2}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{1}{2}$

Decimal Form:

$x = - 0.5$