Question
Simplify the expression without a calculator. \( \log \left(10^{\sqrt{7}}\right)=\square \)
Ask by Peterson Phillips. in the United States
Mar 12,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The simplified expression is \( \sqrt{7} \).
Solution
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Extra Insights
To simplify the expression \( \log \left(10^{\sqrt{7}}\right) \), you can use the logarithmic property that states \( \log_b (a^c) = c \cdot \log_b (a) \). In this case, we have \( \log \left(10^{\sqrt{7}}\right) = \sqrt{7} \cdot \log (10) \). Since \( \log (10) = 1 \), the expression simplifies to \( \sqrt{7} \cdot 1 = \sqrt{7} \). Therefore, \( \log \left(10^{\sqrt{7}}\right) = \sqrt{7} \). So, the answer is: \(\sqrt{7}\)
