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Popular >

simplify ln(ae^{bt})

Solution

simplify

ln (a e^{b t})

Solution

ln (a) + b t

Solution steps

ln (a e^{b t})

Apply log rule:

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

ln (a e^{b t}) = ln (a) + ln (e^{b t})

= ln (a) + ln (e^{b t})

Apply log rule:

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

ln (e^{b t}) = b t ln (e)

= ln (a) + b t ln (e)

b t ln (e) = b t

= ln (a) + b t

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Frequently Asked Questions (FAQ)

What is ln(ae^{bt}) ?
The solution to ln(ae^{bt}) is ln(a)+bt