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Popular >

simplify log_{e}(5e^{2x})

Solution

simplify

lo g_{e} (5 e^{2 x})

Solution

ln (5) + 2 x

Solution steps

lo g_{e} (5 e^{2 x})

Apply log rule:

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

lo g_{e} (5 e^{2 x}) = lo g_{e} (5) + lo g_{e} (e^{2 x})

= lo g_{e} (5) + lo g_{e} (e^{2 x})

Apply log rule:

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

lo g_{e} (e^{2 x}) = 2 x lo g_{e} (e)

= lo g_{e} (5) + 2 x lo g_{e} (e)

lo g_{e} (5) = ln (5)

2 x lo g_{e} (e) = 2 x

= ln (5) + 2 x

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Frequently Asked Questions (FAQ)

What is log_{e}(5e^{2x}) ?
The solution to log_{e}(5e^{2x}) is ln(5)+2x