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### Question 5: Solve the following equations, giving your answers to 2 decimal places where appropriate.
**(a)** \( 4^{5 - x} = 11^{2x - 1} \)

**(b)** \( 2^{2x + 1} - 12^{x} - 6 = 0 \)

**(c)** \( 3(16^{5}) - 4^{x + 2} + 5 = 0 \)

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Would you like to start solving one of these equations? If yes, let me know which one! 

Here are five follow-up questions to deepen your understanding:
1. What is the general process for solving exponential equations?
2. How do logarithmic properties assist in solving exponential equations like (a)?
3. What strategies can be used to simplify complex exponents like in (c)?
4. Can you explain why taking the logarithm of both sides of an equation is useful?
5. How does the base of an exponential function affect the solution of the equation?

**Tip**: Always try to express both sides of an equation with the same base when possible—it makes solving much easier!

Solve the following equations, giving your answers to 2 decimal places where appropriate: (a) 4^(5 - x) = 11^(2x - 1) (b) 2^(2x + 1) - 12^x - 6 = 0 (c) 3(16^5) - 4^(x + 2) + 5 = 0

Learn how to solve complex exponential equations such as 4^(5 - x) = 11^(2x - 1), using logarithms and properties of exponents. This tutorial walks through detailed steps and key concepts, including logarithmic transformations. Suitable for high school students, Grades 10-12.

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