What is ln((w^5x^{4/5})/(y^8z^7)) ?

The solution to ln((w^5x^{4/5})/(y^8z^7)) is 5ln(w)+4/5 ln(x)-8ln(y)-7ln(z)

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simplify ln((w^5x^{4/5})/(y^8z^7))

simplify

ln (\frac{w ^{5} x ^{\frac{4}{5}}}{y ^{8} z ^{7}})

5 ln (w) + \frac{4}{5} ln (x) - 8 ln (y) - 7 ln (z)

Solution steps

ln (\frac{w ^{5} x ^{\frac{4}{5}}}{y ^{8} z ^{7}})

Apply log rule:

lo g_{c} (\frac{a}{b}) = lo g_{c} (a) - lo g_{c} (b)

ln (\frac{w ^{5} x ^{\frac{4}{5}}}{y ^{8} z ^{7}}) = ln (w^{5} x^{\frac{4}{5}}) - ln (y^{8} z^{7})

= ln (w^{5} x^{\frac{4}{5}}) - ln (y^{8} z^{7})

Apply log rule:

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

ln (w^{5} x^{\frac{4}{5}}) = ln (w^{5}) + ln (x^{\frac{4}{5}}), ln (y^{8} z^{7}) = ln (y^{8}) + ln (z^{7})

= ln (w^{5}) + ln (x^{\frac{4}{5}}) - (ln (y^{8}) + ln (z^{7}))

Apply log rule:

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

ln (w^{5}) = 5 ln (w)

= 5 ln (w) + ln (x^{\frac{4}{5}}) - (ln (y^{8}) + ln (z^{7}))

Apply log rule:

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

ln (x^{\frac{4}{5}}) = \frac{4}{5} ln (x)

= 5 ln (w) + \frac{4}{5} ln (x) - (ln (y^{8}) + ln (z^{7}))

Apply log rule:

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

ln (y^{8}) = 8 ln (y)

= 5 ln (w) + \frac{4}{5} ln (x) - (8 ln (y) + ln (z^{7}))

Apply log rule:

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

ln (z^{7}) = 7 ln (z)

= 5 ln (w) + \frac{4}{5} ln (x) - (8 ln (y) + 7 ln (z))

- (8 ln (y) + 7 ln (z)) : - 8 ln (y) - 7 ln (z)

= 5 ln (w) + \frac{4}{5} ln (x) - 8 ln (y) - 7 ln (z)

lo g_{9} (\frac{x}{81})

lo g_{2 x - 1} (4.5 x)

lo g_{10} (\frac{x}{1 0 ^{- 12}})

ln (1 \cdot 5)

What is ln((w^5x^{4/5})/(y^8z^7)) ?
The solution to ln((w^5x^{4/5})/(y^8z^7)) is 5ln(w)+4/5 ln(x)-8ln(y)-7ln(z)