To solve the equation $$ 10^{x} = 33 $$ for $$ x $$, you can use logarithms. Here's a step-by-step solution: 1. **Take the logarithm of both sides:** You can use either the common logarithm (base 10) or the natural logarithm (base $$ e $$). Here, we'll use the common logarithm for simplicity. \[ \log_{10}(10^{x}) = \log_{10}(33) \] 2. **Apply the logarithm power rule:** The logarithm power rule states that $$ \log_{b}(a^{c}) = c \cdot \log_{b}(a) $$. Applying this rule: \[ x \cdot \log_{10}(10) = \log_{10}(33) \] 3. **Simplify the equation:** Since $$ \log_{10}(10) = 1 $$: \[ x = \log_{10}(33) \] 4. **Calculate the numerical value:** Using a calculator to find $$ \log_{10}(33) $$: \[ x \approx 1.5185 \] Therefore, \[ x \approx 1.5185 \] **Final Answer:** The solution is $$ x = \log_{10}(33) \approx 1.5185 $$. $$ x = \log_{10}(33) \approx 1.5185 $$

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10. $ 10^{x}=33 $

Ask by Cook Mitchell. in the United States

Jan 21,2025

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$ x = \log_{10}(33) \approx 1.5185 $

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Beyond the Answer

To solve the equation $ 10^{x} = 33 $, take the logarithm of both sides. This gives you $ x = \log_{10}(33) $. You can use a calculator or logarithm table to find that $ \log_{10}(33) $ is approximately 1.5185. So, $ x $ is about 1.5185! And here's a fun math tip: whenever you're stuck on exponential equations, remember that logarithms are your best friends! They help you convert those pesky exponents into manageable numbers, making solving much easier. Just keep practicing, and you'll conquer those exponential equations like a pro!

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