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Popular >

simplify ln(z^4e^{2z})

Solution

simplify

ln (z^{4} e^{2 z})

Solution

4 ln (z) + 2 z

Solution steps

ln (z^{4} e^{2 z})

Apply log rule:

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

ln (z^{4} e^{2 z}) = ln (z^{4}) + ln (e^{2 z})

= ln (z^{4}) + ln (e^{2 z})

Apply log rule:

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

ln (z^{4}) = 4 ln (z)

= 4 ln (z) + ln (e^{2 z})

Apply log rule:

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

ln (e^{2 z}) = 2 z ln (e)

= 4 ln (z) + 2 z ln (e)

2 z ln (e) = 2 z

= 4 ln (z) + 2 z

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Frequently Asked Questions (FAQ)

What is ln(z^4e^{2z}) ?
The solution to ln(z^4e^{2z}) is 4ln(z)+2z