What is 1/2 (3ln(x)-5ln(y)) ?

The solution to 1/2 (3ln(x)-5ln(y)) is 1/2 ln((x^3)/(y^5))

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simplify 1/2 (3ln(x)-5ln(y))

simplify

\frac{1}{2} (3 ln (x) - 5 ln (y))

\frac{1}{2} ln (\frac{x ^{3}}{y ^{5}})

Solution steps

\frac{1}{2} (3 ln (x) - 5 ln (y))

Apply log rule:

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

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

= \frac{1}{2} (ln (x^{3}) - 5 ln (y))

Apply log rule:

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

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

= \frac{1}{2} (ln (x^{3}) - ln (y^{5}))

Apply log rule:

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

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

= \frac{1}{2} ln (\frac{x ^{3}}{y ^{5}})

0.0296 (46 e^{(\frac{l n ( 263 ) - l n ( 46 )}{30}) \cdot 1})

ln (\frac{4.79526}{- 4.92})

\frac{1}{3} ln (6)

- 0.8 \cdot lo g_{2} (0.8) - 0.2 \cdot lo g_{2} (0.2)

- lo g_{10} (1.3 \cdot 1 0^{6})

What is 1/2 (3ln(x)-5ln(y)) ?
The solution to 1/2 (3ln(x)-5ln(y)) is 1/2 ln((x^3)/(y^5))