What is ln((2a^3)/(b^4)) ?

The solution to ln((2a^3)/(b^4)) is ln(2)+3ln(a)-4ln(b)

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simplify ln((2a^3)/(b^4))

simplify

ln (\frac{2 a ^{3}}{b ^{4}})

ln (2) + 3 ln (a) - 4 ln (b)

Solution steps

ln (\frac{2 a ^{3}}{b ^{4}})

Apply log rule:

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

ln (\frac{2 a ^{3}}{b ^{4}}) = ln (2 a^{3}) - ln (b^{4})

= ln (2 a^{3}) - ln (b^{4})

Apply log rule:

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

ln (b^{4}) = 4 ln (b)

= ln (2 a^{3}) - 4 ln (b)

Apply log rule:

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

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

= ln (2) + ln (a^{3}) - 4 ln (b)

Apply log rule:

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

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

= ln (2) + 3 ln (a) - 4 ln (b)

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What is ln((2a^3)/(b^4)) ?
The solution to ln((2a^3)/(b^4)) is ln(2)+3ln(a)-4ln(b)