Questions: 4(10^(x-2))+3=2,021

4(10^(x-2))+3=2,021
Transcript text: $4\left(10^{x-2}\right)+3=2,021$
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Solution

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Solution Steps

To solve the equation \(4(10^{x-2}) + 3 = 2,021\), we first isolate the term with the exponent by subtracting 3 from both sides. Then, divide by 4 to solve for \(10^{x-2}\). Finally, take the logarithm to solve for \(x\).

Step 1: Isolate the Exponential Term

Start with the equation: \[ 4(10^{x-2}) + 3 = 2,021 \]

Subtract 3 from both sides: \[ 4(10^{x-2}) = 2,018 \]

Divide by 4: \[ 10^{x-2} = 504.5 \]

Step 2: Solve for \(x\)

Take the logarithm base 10 of both sides: \[ x - 2 = \log_{10}(504.5) \]

Calculate \(\log_{10}(504.5)\): \[ x - 2 \approx 2.7029 \]

Add 2 to both sides: \[ x \approx 4.7029 \]

Final Answer

\[ \boxed{x \approx 4.7029} \]

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