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Popular >

simplify ln(ae^{bx})

Solution

simplify

ln (a \cdot e^{b \cdot x})

Solution

ln (a) + b x

Solution steps

ln (a e^{b x})

Apply log rule:

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

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

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

Apply log rule:

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

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

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

b x ln (e) = b x

= ln (a) + b x

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Frequently Asked Questions (FAQ)

What is ln(a*e^{b*x}) ?
The solution to ln(a*e^{b*x}) is ln(a)+bx