Question

In the following exercises, solve.

$(5x-4{)}^{\frac{1}{4}}+7=9$

Short answer

The solution of the given equation is $x=4$.

Step-by-step solution

Step 1. Given information.

The given equation is:

$(5x-4{)}^{\frac{1}{4}}+7=9$

Step 2. Solve the equation.

The given equation can be written as:

$\begin{array}{rcl}(5x-4{)}^{\frac{1}{4}}& =& 9-7\\ (5x-4{)}^{\frac{1}{4}}& =& 2\end{array}$

Take power 4 on both sides.

$\begin{array}{rcl}5x-4& =& (2{)}^4\\ 5x& =& 16+4\\ x& =& \frac{20}{5}\\ x& =& 4\end{array}$

Step 3. Conclusion.

The solution of the given equation is $x=4$.