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Popular >

simplify ln(3e^{2θ})

Solution

simplify

ln (3 e^{2 θ})

Solution

ln (3) + 2 θ

Solution steps

ln (3 e^{2 θ})

Apply log rule:

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

ln (3 e^{2 θ}) = ln (3) + ln (e^{2 θ})

= ln (3) + ln (e^{2 θ})

Apply log rule:

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

ln (e^{2 θ}) = 2 θ ln (e)

= ln (3) + 2 θ ln (e)

2 θ ln (e) = 2 θ

= ln (3) + 2 θ

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Frequently Asked Questions (FAQ)

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