Logarithms

Can someone explain to me why ln e^5 equals 5?

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  1. ln 2.7185 = ln 148.413 = 5

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  2. ln (e^5 )= 5 ln e
    but ln e = 1
    so ln (e^5) = 5*1 = 5

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  3. How do you solve 4 to the power of 2-6x = 812? I can't find a common number that raised to a power equals 812.

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