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Popular >

simplify ln(12e^{x/3})

Solution

simplify

ln (12 e^{\frac{x}{3}})

Solution

ln (12) + \frac{x}{3}

Solution steps

ln (12 e^{\frac{x}{3}})

Apply log rule:

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

ln (12 e^{\frac{x}{3}}) = ln (12) + ln (e^{\frac{x}{3}})

= ln (12) + ln (e^{\frac{x}{3}})

Apply log rule:

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

ln (e^{\frac{x}{3}}) = \frac{x}{3} ln (e)

= ln (12) + \frac{x}{3} ln (e)

\frac{x}{3} ln (e) = \frac{x}{3}

= ln (12) + \frac{x}{3}

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Frequently Asked Questions (FAQ)

What is ln(12e^{x/3}) ?
The solution to ln(12e^{x/3}) is ln(12)+x/3