What is simplify-ln(|x+4|^{15}|3x+2|)-(68)/(x+4) ?

The solution to simplify-ln(|x+4|^{15}|3x+2|)-(68)/(x+4) is -15ln|x+4|-ln|3x+2|-(68)/(x+4)

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simplify-ln(|x+4|^{15}|3x+2|)-(68)/(x+4)

simplify

- ln (∣ x + 4 ∣^{15} ∣ 3 x + 2 ∣) - \frac{68}{x + 4}

- 15 ln ∣ x + 4 ∣ - ln ∣ 3 x + 2 ∣ - \frac{68}{x + 4}

Solution steps

- ln (∣ x + 4 ∣^{15} ∣ 3 x + 2 ∣) - \frac{68}{x + 4}

Apply log rule:

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

ln (∣ x + 4 ∣^{15} ∣ 3 x + 2 ∣) = ln (∣ x + 4 ∣^{15}) + ln ∣ 3 x + 2 ∣

= - (ln (∣ x + 4 ∣^{15}) + ln ∣ 3 x + 2 ∣) - \frac{68}{x + 4}

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

ln (∣ x + 4 ∣^{15}) = 15 ln ∣ x + 4 ∣

= - (15 ln ∣ x + 4 ∣ + ln ∣ 3 x + 2 ∣) - \frac{68}{x + 4}

- (15 ln ∣ x + 4 ∣ + ln ∣ 3 x + 2 ∣) : - 15 ln ∣ x + 4 ∣ - ln ∣ 3 x + 2 ∣

= - 15 ln ∣ x + 4 ∣ - ln ∣ 3 x + 2 ∣ - \frac{68}{x + 4}

\frac{( 6 ln ( x ) + 16 - 6 ln ( 4 ) )}{x}

- ln (0.8) + 2 ln (0.75) - 8 ln (0.65) + ln (0.6)

2 lo g_{5} (x) + 4 (lo g_{5} (y) - 2 lo g_{5} (z))

- ln (\frac{C}{V})

ln (2258064 \cdot 1 0^{- 5})

What is simplify-ln(|x+4|^{15}|3x+2|)-(68)/(x+4) ?
The solution to simplify-ln(|x+4|^{15}|3x+2|)-(68)/(x+4) is -15ln|x+4|-ln|3x+2|-(68)/(x+4)