What is ln(z^4e^{2x}) ?

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

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

simplify

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

4 ln (z) + 2 x

Solution steps

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

Apply log rule:

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

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

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

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 x})

Apply log rule:

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

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

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

2 x ln (e) = 2 x

= 4 ln (z) + 2 x

ln (x + 1) + \frac{1}{2} ln (2 + 3 (\frac{y - 1}{x + 1})^{2})

lo g_{10} (\frac{5 \cdot 1 0 ^{- 6}}{1 \cdot 1 0 ^{- 12}})

(\frac{1}{2})^{2} - \frac{1}{2} - ln (\frac{1}{2})

ln (\frac{16384 x ^{12} + 4}{0.1})

ln (0.023) - ln (0.02)