What is ln((2e^x)/(3x)) ?

The solution to ln((2e^x)/(3x)) is ln(2)+x-ln(3)-ln(x)

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simplify ln((2e^x)/(3x))

simplify

ln (\frac{2 e ^{x}}{3 x})

ln (2) + x - ln (3) - ln (x)

Solution steps

ln (\frac{2 e ^{x}}{3 x})

Apply log rule:

lo g_{c} (\frac{a}{b}) = lo g_{c} (a) - lo g_{c} (b)

ln (\frac{2 e ^{x}}{3 x}) = ln (2 e^{x}) - ln (3 x)

= ln (2 e^{x}) - ln (3 x)

Apply log rule:

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

ln (2 e^{x}) = ln (2) + ln (e^{x}), ln (3 x) = ln (3) + ln (x)

= ln (2) + ln (e^{x}) - (ln (x) + ln (3))

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

ln (e^{x}) = x ln (e)

= ln (2) + x ln (e) - (ln (3) + ln (x))

x ln (e) = x

= ln (2) + x - (ln (x) + ln (3))

- (ln (3) + ln (x)) : - ln (3) - ln (x)

= ln (2) + x - ln (3) - ln (x)

ln (R e^{iπ})

lo g_{9} (- 3 x) + lo g_{9} (- 10 x)

3 ln (4) - ln (16) + ln (3)

\frac{2}{5} lo g_{10} (778)

ln (e^{l n (x)} (e^{l n (e x)}))

What is ln((2e^x)/(3x)) ?
The solution to ln((2e^x)/(3x)) is ln(2)+x-ln(3)-ln(x)