What is simplify-2ln(2a)-2ln(a) ?

The solution to simplify-2ln(2a)-2ln(a) is -ln(4a^4)

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simplify-2ln(2a)-2ln(a)

simplify

- 2 ln (2 a) - 2 ln (a)

- ln (4 a^{4})

Solution steps

- 2 ln (2 a) - 2 ln (a)

Apply log rule:

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

2 ln (2 a) = ln ((2 a)^{2})

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

Apply log rule:

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

2 ln (a) = ln (a^{2})

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

Rewrite

- ln ((2 a)^{2}) - ln (a^{2})

- (ln ((2 a)^{2}) + ln (a^{2}))

= - (ln (a^{2}) + ln ((2 a)^{2}))

Apply log rule:

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

ln ((2 a)^{2}) + ln (a^{2}) = ln (a^{2} (2 a)^{2})

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

Simplify

(2 a)^{2} a^{2} : 4 a^{4}

= - ln (4 a^{4})

ln ∣ 7 ∣ - ln ∣ 0.5 ∣

ln (\frac{19}{15})

ln (\frac{n !}{x ! ( n - x ) !} \cdot p^{x} \cdot (1 - p)^{(n - x)})

- lo g_{10} (6.9 \cdot 1 0^{- 9})

ln (q) - ln (s)

What is simplify-2ln(2a)-2ln(a) ?
The solution to simplify-2ln(2a)-2ln(a) is -ln(4a^4)