What is 2ln(+ln(c)-3ln(5c)) ?

The solution to 2ln(+ln(c)-3ln(5c)) is 2ln(-ln(125c^2))

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simplify 2ln(+ln(c)-3ln(5c))

simplify

2 ln (+ ln (c) - 3 ln (5 c))

2 ln (- ln (125 c^{2}))

Solution steps

2 ln (ln (c) - 3 ln (5 c))

Apply log rule:

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

3 ln (5 c) = ln ((5 c)^{3})

= 2 ln (ln (c) - ln ((5 c)^{3}))

Apply log rule:

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

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

= 2 ln (ln (\frac{c}{( 5 c ) ^{3}}))

Simplify

\frac{c}{( 5 c ) ^{3}} : \frac{1}{125 c ^{2}}

= 2 ln (ln (\frac{1}{125 c ^{2}}))

Simplify

ln (\frac{1}{125 c ^{2}}) : - ln (125 c^{2})

= 2 ln (- ln (125 c^{2}))

ln (3 x)

ln (\frac{x}{120})

ln (\frac{326.48}{373})

2 - 9 \cdot ln (\frac{1 + 2}{2})

6 ln (2 \frac{2 ^{2}}{2})

What is 2ln(+ln(c)-3ln(5c)) ?
The solution to 2ln(+ln(c)-3ln(5c)) is 2ln(-ln(125c^2))