What is ln(((-6e^{5x}))/5) ?

The solution to ln(((-6e^{5x}))/5) is ln(6)+5x-ln(5)

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simplify ln(((-6e^{5x}))/5)

simplify

ln (\frac{( - 6 e ^{5 x} )}{5})

ln (6) + 5 x - ln (5)

Solution steps

ln (\frac{( - 6 e ^{5 x} )}{5})

Apply log rule:

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

ln (\frac{( - 6 e ^{5 x} )}{5}) = ln ((- 6 e^{5 x})) - ln (5)

= ln (- 6 e^{5 x}) - ln (5)

Apply log rule:

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

ln (- 6 e^{5 x}) = ln (6) + ln (e^{5 x})

= ln (6) + ln (e^{5 x}) - ln (5)

Apply log rule:

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

ln (e^{5 x}) = 5 x ln (e)

= ln (6) + 5 x ln (e) - ln (5)

5 x ln (e) = 5 x

= ln (6) + 5 x - ln (5)

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What is ln(((-6e^{5x}))/5) ?
The solution to ln(((-6e^{5x}))/5) is ln(6)+5x-ln(5)