What is simplify-ln((2l+d)/l)+ln((l+d)/l)+ln((l+d)/d) ?

The solution to simplify-ln((2l+d)/l)+ln((l+d)/l)+ln((l+d)/d) is ln(((l+d)^2)/(d(2l+d)))

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simplify-ln((2l+d)/l)+ln((l+d)/l)+ln((l+d)/d)

simplify

- ln (\frac{2 l + d}{l}) + ln (\frac{l + d}{l}) + ln (\frac{l + d}{d})

ln (\frac{( l + d ) ^{2}}{d ( 2 l + d )})

Solution steps

- ln (\frac{2 l + d}{l}) + ln (\frac{l + d}{l}) + ln (\frac{l + d}{d})

Apply log rule:

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

ln (\frac{l + d}{l}) - ln (\frac{2 l + d}{l}) = ln (\frac{\frac{d + l}{l}}{\frac{d + 2 l}{l}})

= ln (\frac{\frac{d + l}{l}}{\frac{d + 2 l}{l}}) + ln (\frac{d + l}{d})

Simplify

\frac{\frac{l + d}{l}}{\frac{2 l + d}{l}} : \frac{l + d}{2 l + d}

= ln (\frac{l + d}{2 l + d}) + ln (\frac{l + d}{d})

Apply log rule:

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

ln (\frac{l + d}{2 l + d}) + ln (\frac{l + d}{d}) = ln (\frac{d + l}{d} \cdot \frac{d + l}{d + 2 l})

= ln (\frac{d + l}{d} \cdot \frac{d + l}{d + 2 l})

Simplify

\frac{l + d}{2 l + d} \cdot \frac{l + d}{d} : \frac{( l + d ) ^{2}}{d ( 2 l + d )}

= ln (\frac{( l + d ) ^{2}}{d ( 2 l + d )})

- lo g_{10} (7.93 \cdot 1 0^{- 3})

\frac{2}{7} lo g_{10} (a) - \frac{1}{8} lo g_{10} (b)

ln (ln (y)) + ln (x) + c

ln (\frac{432}{5})

lo g_{10} ((\frac{x}{y ^{4}})^{4})

What is simplify-ln((2l+d)/l)+ln((l+d)/l)+ln((l+d)/d) ?
The solution to simplify-ln((2l+d)/l)+ln((l+d)/l)+ln((l+d)/d) is ln(((l+d)^2)/(d(2l+d)))