What is ln((a^2)/b)+ln(ab)+ln(a^3) ?

The solution to ln((a^2)/b)+ln(ab)+ln(a^3) is 2ln(a^3)

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simplify ln((a^2)/b)+ln(ab)+ln(a^3)

simplify

ln (\frac{a ^{2}}{b}) + ln (ab) + ln (a^{3})

2 ln (a^{3})

Solution steps

ln (\frac{a ^{2}}{b}) + ln (ab) + ln (a^{3})

Apply log rule:

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

ln (\frac{a ^{2}}{b}) + ln (ab) = ln (ab \frac{a ^{2}}{b})

= ln (ab \frac{a ^{2}}{b}) + ln (a^{3})

Simplify

\frac{a ^{2}}{b} ab : a^{3}

= ln (a^{3}) + ln (a^{3})

Add similar elements:

ln (a^{3}) + ln (a^{3}) = 2 ln (a^{3})

= 2 ln (a^{3})

ln (x \times y)

lo g_{3} (\frac{7}{13})

lo g_{4} (5 x^{3} y)

lo g_{10} (\frac{x ^{3}}{y})

What is ln((a^2)/b)+ln(ab)+ln(a^3) ?
The solution to ln((a^2)/b)+ln(ab)+ln(a^3) is 2ln(a^3)