Question

Solve the equation with rational exponents. Check all proposed solutions

Answer 1

We need to solve the following equation

$7x^{\frac{7}{2}}-21=0$

Steps:

1. Add 21 to both sides

$7x^{\frac{7}{2}}=21$

2. Divide both sides by 7

$x^{\frac{7}{2}}=3$

3. apply the following

$\begin{gathered} \ln x^{\frac{7}{2}}=\ln 3 \\ \frac{7}{2}\ln x=\ln 3 \\ \ln x=\frac{2}{7}\ln 3 \\ e^{\ln x}=e^{(\frac{2}{7}\ln 3)} \\ x=3^{\frac{2}{7}} \end{gathered}$

Thus, the solution is

$x=3^{\frac{2}{7}}$