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Popular >

simplify ln(3e^{1/2 x})

Solution

simplify

ln (3 e^{\frac{1}{2} x})

Solution

ln (3) + \frac{x}{2}

Solution steps

ln (3 e^{\frac{1}{2} x})

Apply log rule:

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

ln (3 e^{\frac{1}{2} x}) = ln (3) + ln (e^{\frac{1}{2} x})

= ln (3) + ln (e^{\frac{1}{2} x})

Apply log rule:

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

ln (e^{\frac{1}{2} x}) = \frac{1}{2} x ln (e)

= ln (3) + \frac{1}{2} x ln (e)

\frac{1}{2} x ln (e) = \frac{x}{2}

= ln (3) + \frac{x}{2}

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Frequently Asked Questions (FAQ)

What is ln(3e^{1/2 x}) ?
The solution to ln(3e^{1/2 x}) is ln(3)+x/2