What is ln((x^3z^5)/(y^7)) ?

The solution to ln((x^3z^5)/(y^7)) is 3ln(x)+5ln(z)-7ln(y)

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simplify ln((x^3z^5)/(y^7))

simplify

ln (\frac{x ^{3} z ^{5}}{y ^{7}})

3 ln (x) + 5 ln (z) - 7 ln (y)

Solution steps

ln (\frac{x ^{3} z ^{5}}{y ^{7}})

Apply log rule:

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

ln (\frac{x ^{3} z ^{5}}{y ^{7}}) = ln (x^{3} z^{5}) - ln (y^{7})

= ln (x^{3} z^{5}) - ln (y^{7})

Apply log rule:

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

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

= ln (x^{3} z^{5}) - 7 ln (y)

Apply log rule:

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

ln (x^{3} z^{5}) = ln (x^{3}) + ln (z^{5})

= ln (x^{3}) + ln (z^{5}) - 7 ln (y)

Apply log rule:

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

ln (x^{3}) = 3 ln (x)

= 3 ln (x) + ln (z^{5}) - 7 ln (y)

Apply log rule:

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

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

= 3 ln (x) + 5 ln (z) - 7 ln (y)

- lo g_{10} (6.17 \cdot 1 0^{- 5})

4 ln (y) - 3 ln (x) + \frac{y}{x}

ln (z x^{2} \cdot y^{5})

ln (x + 2) + ln (x + 1)

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

What is ln((x^3z^5)/(y^7)) ?
The solution to ln((x^3z^5)/(y^7)) is 3ln(x)+5ln(z)-7ln(y)