What is 1/2 ln(x)+4ln(y)-7ln(z) ?

The solution to 1/2 ln(x)+4ln(y)-7ln(z) is ln((x^{1/2}y^4)/(z^7))

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simplify 1/2 ln(x)+4ln(y)-7ln(z)

simplify

\frac{1}{2} ln (x) + 4 ln (y) - 7 ln (z)

ln (\frac{x ^{\frac{1}{2}} y ^{4}}{z ^{7}})

Solution steps

\frac{1}{2} ln (x) + 4 ln (y) - 7 ln (z)

Apply log rule:

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

\frac{1}{2} ln (x) = ln (x^{\frac{1}{2}})

= ln (x^{\frac{1}{2}}) + 4 ln (y) - 7 ln (z)

Apply log rule:

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

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

= ln (x^{\frac{1}{2}}) + ln (y^{4}) - 7 ln (z)

Apply log rule:

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

ln (x^{\frac{1}{2}}) + ln (y^{4}) = ln (y^{4} x^{\frac{1}{2}})

= ln (x^{\frac{1}{2}} y^{4}) - 7 ln (z)

Apply log rule:

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

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

= ln (y^{4} x^{\frac{1}{2}}) - ln (z^{7})

Apply log rule:

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

ln (y^{4} x^{\frac{1}{2}}) - ln (z^{7}) = ln (\frac{y ^{4} x ^{\frac{1}{2}}}{z ^{7}})

= ln (\frac{x ^{\frac{1}{2}} y ^{4}}{z ^{7}})

lo g_{4} (5) - lo g_{4} (7)

lo g_{7} ((\frac{u w}{v ^{4}})^{6})

ln (7 x) - ln (7)

ln (\frac{e ^{x}}{x ^{7}})

lo g_{a} (\frac{x ^{8}}{y z ^{9}})

What is 1/2 ln(x)+4ln(y)-7ln(z) ?
The solution to 1/2 ln(x)+4ln(y)-7ln(z) is ln((x^{1/2}y^4)/(z^7))