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

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

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

expand

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)

lo g_{5} (4 x^{2})

ln ((x + h)^{2} + (x + h) + 1) - ln (x^{2} + x + 1)

ln (\frac{2 \cdot 22.91}{0.01173})

ln (\frac{100}{1435})

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