Question 202936
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*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 12^{\sqrt{x}}=35]


Take the log of both sides:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \ln(12^{\sqrt{x}})=\ln(35)]


Use:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \log_b(x^n) = n\log_b(x)]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \sqrt{x}\ln(12)=\ln(35)]


Divide both sides by *[tex \Large \ln(12)]:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \sqrt{x} = \frac{\ln(35)}{\ln(12)]


Square both sides:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x = \left(\frac{\ln(35)}{\ln(12)\right)^2]


None of the given answers actually says that, unless that is what you meant by the representation in answer a.


John
*[tex \LARGE e^{i\pi} + 1 = 0]
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