What is 5ln(x)+2ln(y)-ln(z) ?

The solution to 5ln(x)+2ln(y)-ln(z) is ln((x^5y^2)/z)

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simplify 5ln(x)+2ln(y)-ln(z)

simplify

5 ln (x) + 2 ln (y) - ln (z)

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

Solution steps

5 ln (x) + 2 ln (y) - ln (z)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

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

= ln (x^{5}) + 2 ln (y) - ln (z)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

2 ln (y) = ln (y^{2})

= ln (x^{5}) + ln (y^{2}) - ln (z)

Apply log rule:

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

ln (x^{5}) + ln (y^{2}) = ln (x^{5} y^{2})

= ln (x^{5} y^{2}) - ln (z)

Apply log rule:

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

ln (x^{5} y^{2}) - ln (z) = ln (\frac{x ^{5} y ^{2}}{z})

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

ln (4 \cdot 1 0^{- 6})

lo g_{10} (2 ln (- 1))

ln (x (y + 2)^{2})

ln (\frac{30}{21.35})

ln (2) + ln (\frac{π}{2})

What is 5ln(x)+2ln(y)-ln(z) ?
The solution to 5ln(x)+2ln(y)-ln(z) is ln((x^5y^2)/z)