What is ln(-6sqrt((e^{(x)))/3}) ?

The solution to ln(-6sqrt((e^{(x)))/3}) is ln(6)+ln(sqrt((e^x)/3))

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simplify ln(-6sqrt((e^{(x)))/3})

simplify

ln (- 6 \frac{e ^{(x)}}{3})

ln (6) + ln (\frac{e ^{x}}{3})

Solution steps

ln (- 6 \frac{e ^{(x)}}{3})

Apply log rule:

lo g_{c} (ab) = lo g_{c} (a) + lo g_{c} (b)

ln (- 6 \frac{e ^{(x)}}{3}) = ln (6) + ln (\frac{e ^{(x)}}{3})

= ln (6) + ln (\frac{e ^{(x)}}{3})

Remove parentheses:

(a) = a

= ln (6) + ln (\frac{e ^{x}}{3})

ln (1^{2} (1 + 2)^{\frac{9}{5}} (1 - 3)^{\frac{1}{5}})

3 ln (4) - \frac{1}{2} ln (x^{2} + 3)

\frac{3}{5} lo g_{\frac{4}{25}} (5) - \frac{3}{5} lo g_{\frac{4}{25}} (2)

\frac{3}{4} \cdot lo g_{2} (\frac{( \frac{3}{4} )}{( \frac{1}{20} )})

\frac{8}{π} \cdot ln (6) + \frac{2}{π} \cdot ln (\frac{7}{6})

What is ln(-6sqrt((e^{(x)))/3}) ?
The solution to ln(-6sqrt((e^{(x)))/3}) is ln(6)+ln(sqrt((e^x)/3))