What is 1+3ln(x)-4ln(y)-0.5ln(z) ?

The solution to 1+3ln(x)-4ln(y)-0.5ln(z) is 1+ln((x^3)/(y^4z^{0.5)})

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simplify 1+3ln(x)-4ln(y)-0.5ln(z)

simplify

1 + 3 ln (x) - 4 ln (y) - 0.5 ln (z)

1 + ln (\frac{x ^{3}}{y ^{4} z ^{0.5}})

Solution steps

1 + 3 ln (x) - 4 ln (y) - 0.5 ln (z)

Apply log rule:

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

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

= 1 + ln (x^{3}) - 4 ln (y) - 0.5 ln (z)

Apply log rule:

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

4 ln (y) = ln (y^{4})

= 1 + ln (x^{3}) - ln (y^{4}) - 0.5 ln (z)

Apply log rule:

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

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

= 1 + ln (\frac{x ^{3}}{y ^{4}}) - 0.5 ln (z)

Apply log rule:

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

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

= 1 + ln (\frac{x ^{3}}{y ^{4}}) - ln (z^{0.5})

Apply log rule:

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

ln (\frac{x ^{3}}{y ^{4}}) - ln (z^{0.5}) = ln (\frac{\frac{x ^{3}}{y ^{4}}}{z ^{0.5}})

= 1 + ln (\frac{\frac{x ^{3}}{y ^{4}}}{z ^{0.5}})

Apply the fraction rule:

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

= 1 + ln (\frac{x ^{3}}{y ^{4} z ^{0.5}})

ln (\frac{- 1 + e ^{t}}{e ^{t} - 2})

ln ((2 x + 1) (x - 4))

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

ln (3 - 2 x) - 2 ln (x)

ln (\frac{2}{72})

What is 1+3ln(x)-4ln(y)-0.5ln(z) ?
The solution to 1+3ln(x)-4ln(y)-0.5ln(z) is 1+ln((x^3)/(y^4z^{0.5)})