Questions: Rearrange this equation to isolate A. H ≡ K + log (A/C)

Rearrange this equation to isolate A. H ≡ K + log (A/C)
Transcript text: Rearrange this equation to isolate A. \[ H \equiv K+\log \left(\frac{A}{C}\right) \]
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Solution

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Solution Steps

To isolate \( A \) in the given equation, we need to perform the following steps:

  1. Subtract \( K \) from both sides to get \( H - K = \log \left(\frac{A}{C}\right) \).
  2. Exponentiate both sides to remove the logarithm, resulting in \( 10^{(H-K)} = \frac{A}{C} \).
  3. Multiply both sides by \( C \) to solve for \( A \).
Step 1: Rearrange the Equation

To isolate \( A \) in the equation \( H \equiv K + \log \left(\frac{A}{C}\right) \), we first subtract \( K \) from both sides: \[ H - K = \log \left(\frac{A}{C}\right) \]

Step 2: Remove the Logarithm

Next, we exponentiate both sides to eliminate the logarithm: \[ 10^{(H-K)} = \frac{A}{C} \]

Step 3: Solve for \( A \)

Finally, we multiply both sides by \( C \) to solve for \( A \): \[ A = C \times 10^{(H-K)} \]

Final Answer

Given the values \( H = 5 \), \( K = 2 \), and \( C = 3 \), we substitute these into the equation: \[ A = 3 \times 10^{(5-2)} = 3 \times 10^3 = 3000 \] Thus, the value of \( A \) is \(\boxed{3000}\).

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