5 Ways To Solving The Exponential Equation 32^y+5 2024

<ul> <li> Solving the Exponential Equation 32^y+5 = 5 Step-by-Step Guide </li> </ul>

Learn how to solve the exponential equation 32^y+5 = 5 for y. Discover the key steps to simplify the equation and find the solution using logarithms.

The video discusses how to solve the exponential equation 32^y+5 = 5 for y.
It emphasizes the conversion of 32 to 2^5 to simplify the equation.
The logarithm is used to solve the equation, and the final solution is presented.

In this instructional video titled "How to Solve Exponential Equation | 32^y+5 = 5 | Solve for y," the presenter provides a step-by-step guide to solve the exponential equation 32^y+5 = 5 for the variable y. The video starts by emphasizing the importance of understanding the relationship between 32 and 2^5, allowing for the equation to be simplified. The presenter then delves into the solution process, explaining how logarithms are used to find the value of y.

Let's break down the key points of the video

Conversion of 32 to 2^5 The video begins by highlighting the relationship between 32 and 2^5. This key insight simplifies the equation, as it allows for the substitution of 32 with 2^5.
Simplifying the Equation With 2^5 as the base, the equation becomes 2^5y+5 = 5. The presenter acknowledges that this is a non-trivial equation, as the bases are different and cannot be easily combined.
Introduction of Logarithms To tackle this complex equation, the presenter introduces logarithms. By taking the logarithm of both sides, the equation becomes log(2^5y+5) = log(5). In this step, it's essential to remember that the base of the logarithm is not specified, so it's assumed to be in base 10.
Applying Logarithm Rules The video demonstrates the application of logarithmic rules, specifically the rule that states log(a^x) = x * log(a). Applying this rule to the equation results in 5y + 25 = log(5).
Isolating y To find the value of y, the presenter simplifies the equation further. They subtract 25 from both sides, which gives 5y = log(5) - 25.
Solving for y Finally, the video concludes by solving for y. To do this, they divide both sides by 5, yielding y = (1/5) * (log(5) - 25). This equation represents the solution to the given exponential equation.

In summary, this video provides a clear and structured approach to solving the exponential equation 32^y+5 = 5. It emphasizes the importance of recognizing the relationship between 32 and 2^5, introduces logarithms as a powerful tool to simplify the equation, and guides viewers through the step-by-step process of finding the solution for y. This instructional content is a valuable resource for anyone seeking to enhance their mathematical problem-solving skills.

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