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Popular >

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

Solution

simplify

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

Solution

2 ln (z) + 4 z

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

4 z ln (e) = 4 z

= 2 ln (z) + 4 z

Popular Examples

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simplify ln(x^2+2x-80)-ln(x-8)simplify

ln (x^{2} + 2 x - 80) - ln (x - 8)

simplify 1/(0.00003)ln((75-15)/(400-15))simplify

\frac{1}{0.00003} ln (\frac{75 - 15}{400 - 15})

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\frac{( ln ( 2.71 ) - ln ( 5.82 ) )}{2}

simplify-log_{10}(3.162*10^{-8})simplify

- lo g_{10} (3.162 \cdot 1 0^{- 8})

Frequently Asked Questions (FAQ)

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