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Popular >

expand ln(αxe^{βx})

Solution

expand

ln (αx e^{β x})

Solution

ln (α) + ln (x) + β x

Solution steps

ln (αx e^{β x})

Apply log rule:

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

ln (αx e^{β x}) = ln (α) + ln (x) + ln (e^{β x})

= ln (α) + ln (x) + ln (e^{β x})

Apply log rule:

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

ln (e^{β x}) = β x ln (e)

= ln (α) + ln (x) + β x ln (e)

β x ln (e) = β x

= ln (α) + ln (x) + β x

Popular Examples

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9 lo g_{135} (- 9 lo g_{5} (x))

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Frequently Asked Questions (FAQ)

What is expand ln(αxe^{βx}) ?
The solution to expand ln(αxe^{βx}) is ln(α)+ln(x)+βx