Questions: Solve the equation. 10^x = 28 x = (Round to four decimal places as needed)

Solve the equation. 10^x = 28 x = (Round to four decimal places as needed)
Transcript text: Solve the equation. \[ 10^{x}=28 \] $x=$ $\square$ (Round to four decimal places as needed)
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Solution

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Solution Steps

To solve the equation \(10^x = 28\), we need to find the value of \(x\). This can be done by taking the logarithm of both sides of the equation. Using the property of logarithms, we can express \(x\) as the logarithm of 28 with base 10.

Step 1: Take the Logarithm

To solve the equation \(10^x = 28\), we take the logarithm of both sides: \[ \log_{10}(10^x) = \log_{10}(28) \]

Step 2: Apply Logarithmic Properties

Using the property of logarithms that states \(\log_{b}(b^a) = a\), we simplify the left side: \[ x = \log_{10}(28) \]

Step 3: Calculate the Value

Calculating the logarithm gives us: \[ x \approx 1.4471580313422192 \] Rounding this to four decimal places, we find: \[ x \approx 1.4472 \]

Final Answer

\(\boxed{x = 1.4472}\)

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