What is ln((-3e^{mx})/(e^{mx)}) ?

The solution to ln((-3e^{mx})/(e^{mx)}) is ln(3)

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simplify ln((-3e^{mx})/(e^{mx)})

simplify

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

ln (3)

Decimal Notation

1.09861 \dots

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Add similar elements:

ln (e) m x - ln (e) m x = 0

= ln (3)

ln (4 kk)

e^{l n (l n (e^{3}))}

- lo g_{10} (0.16 \cdot 1 0^{- 11})

ln (\frac{600}{300})

ln (- \frac{5}{2} e^{2 t})

What is ln((-3e^{mx})/(e^{mx)}) ?
The solution to ln((-3e^{mx})/(e^{mx)}) is ln(3)