Question 330584
<font face="Garamond" size="+2">

*[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
<img src="http://c0rk.blogs.com/gr0undzer0/darwin-fish.jpg">
</font>
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}