Chapter 7.3, Problem 53PPS

To determine

To solve the given equation.

Answer to Problem 53PPS

  $x=8$

Explanation of Solution

Given:

Equation:

  $6^{x-4}=1296$

Calculation:

  $\Rightarrow 6^{x-4}=1296$

  $\Rightarrow 6^{x-4}=(6\times 6\times 6\times 6)$

  $\Rightarrow 6^{x-4}={(6)}^4$

Comparing on both sides,

  $\begin{array}{l}\Rightarrow x-4=4\\ \Rightarrow x=4+4\\ \Rightarrow x=8\end{array}$

Conclusion:

Therefore, the required solution for the given equation is $x=8$ .