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Make ' \( L \) ' the subject of the formula \( A=\sqrt{\frac{E^{2} \ln h}{b}+C-D} \)

Ask by Stuart Williams. in South Africa
Mar 12,2025

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\( L = \frac{b\,(A^{2} - C + D)}{E^{2}} \)

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The Deep Dive

To make \( L \) the subject of the formula, we need to isolate \( L \) on one side of the equation. However, since the formula you've provided does not directly include \( L \) and seems to concern \( A \), \( E \), \( h \), \( b \), \( C \), and \( D \), let's clarify: if \( L \) needs to be expressed in terms of these variables, you might need to start with another equation involving \( L \). For now, here’s what you can understand from \( A = \sqrt{\frac{E^{2} \ln h}{b} + C - D} \): 1. Square both sides: \( A^2 = \frac{E^{2} \ln h}{b} + C - D \). 2. Rearranging gives: \( \frac{E^{2} \ln h}{b} = A^2 + D - C \). 3. Finally, you can express \( \ln h \): \( \ln h = \frac{b(A^2 + D - C)}{E^{2}} \). If you have additional context to involve \( L \), feel free to share for further clarification!

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