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Popular >

simplify ln(-4/5 e^{5x})

Solution

simplify

ln (- \frac{4}{5} e^{5 x})

Solution

2 ln (2) - ln (5) + 5 x

Solution steps

ln (- \frac{4}{5} e^{5 x})

Apply log rule:

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

ln (- \frac{4}{5} e^{5 x}) = ln (\frac{4}{5}) + ln (e^{5 x})

= ln (\frac{4}{5}) + ln (e^{5 x})

Apply log rule:

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

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

= ln (\frac{4}{5}) + 5 x ln (e)

Apply log rule:

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

ln (\frac{4}{5}) = ln (4) - ln (5)

= ln (4) - ln (5) + 5 ln (e) x

5 x ln (e) = 5 x

= ln (4) - ln (5) + 5 x

ln (4) = 2 ln (2)

= 2 ln (2) - ln (5) + 5 x

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Frequently Asked Questions (FAQ)

What is ln(-4/5 e^{5x}) ?
The solution to ln(-4/5 e^{5x}) is 2ln(2)-ln(5)+5x