What is 1/2 (ln(8)x^2-ln(4)-3ln(x)-ln(y)) ?

The solution to 1/2 (ln(8)x^2-ln(4)-3ln(x)-ln(y)) is 1/2 (3ln(2)x^2-ln(4x^3y))

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simplify 1/2 (ln(8)x^2-ln(4)-3ln(x)-ln(y))

simplify

\frac{1}{2} (ln (8) x^{2} - ln (4) - 3 ln (x) - ln (y))

\frac{1}{2} (3 ln (2) x^{2} - ln (4 x^{3} y))

Solution steps

\frac{1}{2} (ln (8) x^{2} - ln (4) - 3 ln (x) - 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 (8) x^{2} - ln (x^{3}) - ln (y) - ln (4))

Rewrite

- ln (4) - ln (x^{3})

- (ln (4) + ln (x^{3}))

= \frac{1}{2} (ln (8) x^{2} - ln (y) - (ln (x^{3}) + ln (4)))

Apply log rule:

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

ln (4) + ln (x^{3}) = ln (4 x^{3})

= \frac{1}{2} (ln (8) x^{2} - ln (4 x^{3}) - ln (y))

Rewrite

- ln (4 x^{3}) - ln (y)

- (ln (4 x^{3}) + ln (y))

= \frac{1}{2} (ln (8) x^{2} - (ln (4 x^{3}) + ln (y)))

Apply log rule:

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

ln (4 x^{3}) + ln (y) = ln (4 x^{3} y)

= \frac{1}{2} (ln (8) x^{2} - ln (4 x^{3} y))

Simplify

ln (8) : 3 ln (2)

= \frac{1}{2} (3 ln (2) x^{2} - ln (4 x^{3} y))

lo g_{3} (x) - lo g_{3} (y) - lo g_{3} (z)

5 lo g_{b} (x) + 6 lo g_{b} (z)

lo g_{10} (3) 2

lo g_{10} (\frac{10}{y})

What is 1/2 (ln(8)x^2-ln(4)-3ln(x)-ln(y)) ?
The solution to 1/2 (ln(8)x^2-ln(4)-3ln(x)-ln(y)) is 1/2 (3ln(2)x^2-ln(4x^3y))