What is ln(0.5*c^{0.5}*z^{0.5}) ?

The solution to ln(0.5*c^{0.5}*z^{0.5}) is ln(0.5)+0.5ln(c)+0.5ln(z)

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simplify ln(0.5c^{0.5}z^{0.5})

simplify

ln (0.5 \cdot c^{0.5} \cdot z^{0.5})

ln (0.5) + 0.5 ln (c) + 0.5 ln (z)

Solution steps

ln (0.5 c^{0.5} z^{0.5})

Apply log rule:

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

ln (0.5 c^{0.5} z^{0.5}) = ln (0.5) + ln (c^{0.5}) + ln (z^{0.5})

= ln (0.5) + ln (c^{0.5}) + ln (z^{0.5})

Apply log rule:

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

ln (c^{0.5}) = 0.5 ln (c)

= ln (0.5) + 0.5 ln (c) + ln (z^{0.5})

Apply log rule:

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

ln (z^{0.5}) = 0.5 ln (z)

= ln (0.5) + 0.5 ln (c) + 0.5 ln (z)

ln (\frac{2 x}{5})

- \frac{5}{4} ln (\frac{0.01}{0.9})

\frac{300}{2 \cdot π \cdot 1200} \cdot ln (\frac{4 + 2 \cdot 120 0 ^{2}}{25})

\frac{- 5 ln ( 5 ) - 4 ln ( 2 )}{7 ln ( 5 ) - ln ( 2 )}

38 \cdot ln (\frac{400}{600}) - 8.314 \cdot ln (\frac{1}{10})

What is ln(0.5*c^{0.5}*z^{0.5}) ?
The solution to ln(0.5*c^{0.5}*z^{0.5}) is ln(0.5)+0.5ln(c)+0.5ln(z)