What is simplify-4ln(-2)-8/3-ln(-3)-3/2 ?

The solution to simplify-4ln(-2)-8/3-ln(-3)-3/2 is -ln(-48)-25/6

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simplify-4ln(-2)-8/3-ln(-3)-3/2

simplify

- 4 ln (- 2) - \frac{8}{3} - ln (- 3) - \frac{3}{2}

- ln (- 48) - \frac{25}{6}

Solution steps

- 4 ln (- 2) - \frac{8}{3} - ln (- 3) - \frac{3}{2}

Apply log rule:

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

4 ln (- 2) = ln ((- 2)^{4})

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

Rewrite

- ln ((- 2)^{4}) - ln (- 3)

- (ln ((- 2)^{4}) + ln (- 3))

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

Apply log rule:

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

ln ((- 2)^{4}) + ln (- 3) = ln ((- 2)^{4} (- 3))

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

(- 2)^{4} (- 3) = - 48

= - ln (- 48) - \frac{8}{3} - \frac{3}{2}

Combine the fractions

- \frac{8}{3} - \frac{3}{2} : - \frac{25}{6}

= - ln (- 48) - \frac{25}{6}

- 2.5 lo g_{10} (7.2346 \cdot 1 0^{10}) + 4.51

- lo g_{10} (2.7 \times 1 0^{- 2})

lo g_{2} (x y^{2})

ln (\frac{e ^{6}}{5})

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

What is simplify-4ln(-2)-8/3-ln(-3)-3/2 ?
The solution to simplify-4ln(-2)-8/3-ln(-3)-3/2 is -ln(-48)-25/6