How do you convert $\frac{1}{3} ln (x) - 3 ln (4) - 5 ln (z)$ $1/3ln(x) - 3 ln (4) - 5 ln(z)$ into a single logarithm?

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Answer 1 · 2015-11-13T15:33:35

$ln (x^{\frac{1}{3}} \cdot \frac{1}{64 z^{5}})$ $ln ( x^{1/3} cdot frac{1}{64z^5} )$

$a ln b = {ln b}^{a}$ $a ln b = ln b^a$

$ln a + ln b = ln (a b)$ $ln a + ln b = ln (ab)$

Expression = $E = ln (x^{\frac{1}{3}}) + {ln 4}^{- 3} + {ln z}^{- 5}$ $E = ln(x^{1/3}) + ln 4^{-3} + ln z^{-5}$

$E = ln (x^{\frac{1}{3}} \cdot 4^{- 3} \cdot z^{- 5})$ $E = ln ( x^{1/3} cdot 4^{-3} cdot z^{-5} )$

How do you convert 13ln(x)−3ln(4)−5ln(z)1/3ln(x) - 3 ln (4) - 5 ln(z) into a single logarithm?