Question
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Answer
\( x = \log_{10}(429) \)
Solution
Solve the equation \( 10^{x}=429 \).
Solve the equation by following steps:
- step0: Solve for \(x\):
\(10^{x}=429\)
- step1: Take the logarithm of both sides:
\(\log_{10}{\left(10^{x}\right)}=\log_{10}{\left(429\right)}\)
- step2: Evaluate the logarithm:
\(x=\log_{10}{\left(429\right)}\)
The solution to the equation \(10^{x}=429\) is \(x=\log_{10}(429)\).
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Simplify this solution Bonus Knowledge
To solve \( 10^{x} = 429 \), you can use logarithms. Take the logarithm of both sides: \[ x = \log_{10}(429) \] Using a calculator, you'll find \( \log_{10}(429) \approx 2.632 \). Thus, \( x \approx 2.632 \) is the solution, which means that \( 10^{2.632} \) gives you approximately 429. Another fun tidbit is that logarithms are widely used in technology and science! For instance, they help us understand measurements on the Richter scale for earthquakes, where each whole number increase represents a tenfold increase in measured amplitude. So, while you solve math problems, you're also tapping into real-world applications!
