202/VB02. problem / Math - Solved Math Problems

MR-202 / 1070a. problem

Solve the following exponential equation:

$16^{\frac{1}{x}} = 4^{\frac{x}{2}}$

Source: Vene T. Bogoslavov: Collection of Solved Problems #2 - 1070.a.)

Algebra → Exponential equations and inequalities → Exponential equations

$16^{\frac{1}{x}} = 4^{\frac{x}{2}}$

16^{\frac{1}{x}} = 4^{\frac{x}{2}}

{(4^{2})}^{\frac{1}{x}} = 4^{\frac{x}{2}}

4^{\frac{2}{x}} = 4^{\frac{x}{2}}

\frac{2}{x} = \frac{x}{2}

4 = x^{2}

x = \pm \sqrt{4}

$x = \pm 2$