What is ln(x)-3ln(z)+0.5ln(y) ?

The solution to ln(x)-3ln(z)+0.5ln(y) is ln((xy^{0.5})/(z^3))

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simplify ln(x)-3ln(z)+0.5ln(y)

simplify

ln (x) - 3 ln (z) + 0.5 ln (y)

ln (\frac{x y ^{0.5}}{z ^{3}})

Solution steps

ln (x) - 3 ln (z) + 0.5 ln (y)

Apply log rule:

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

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

= ln (x) - ln (z^{3}) + 0.5 ln (y)

Apply log rule:

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

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

= ln (\frac{x}{z ^{3}}) + 0.5 ln (y)

Apply log rule:

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

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

= ln (\frac{x}{z ^{3}}) + ln (y^{0.5})

Apply log rule:

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

ln (\frac{x}{z ^{3}}) + ln (y^{0.5}) = ln (\frac{x}{z ^{3}} y^{0.5})

= ln (\frac{x}{z ^{3}} y^{0.5})

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= ln (\frac{x y ^{0.5}}{z ^{3}})

lo g_{10} (x^{5} y^{3} z)

lo g_{10} (\frac{x}{w})

ln (1 \cdot 1 0^{- 3})

ln (100) - ln (101)

ln (e^{3})

What is ln(x)-3ln(z)+0.5ln(y) ?
The solution to ln(x)-3ln(z)+0.5ln(y) is ln((xy^{0.5})/(z^3))