Question 330584
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*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 2\log\left(\sqrt{x}\right)\ +\ 3\log\left(x^{\frac{1}{3}}\right)]

*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 2\log\left(x^{\frac{1}{2}}\right)\ +\ 3\log\left(x^{\frac{1}{3}}\right)]

Use

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

*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 2\,\cdot\,\frac{1}{2}\,\cdot\,\log\left(x\right)\ +\ 3\,\cdot\,\frac{1}{3}\,\cdot\,\log\left(x\right)]

*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \log\left(x\right)\ +\ \log\left(x\right)]

Use the sum of the logs is the log of the product:

*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \log_b(x) + \log_b(y)\ =\ \log_b(xy)]

*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \log\left(x\right)\ +\ \log\left(x\right)\ =\  \log\left(x^2\right)]

If the base is unspecified, the base is 10 by convention:

*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \log_{10}\left(x^2\right)]

John
*[tex \LARGE e^{i\pi} + 1 = 0]
My calculator said it, I believe it, that settles it
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