What is ln((ab^3)/(sqrt(cd^3))) ?

The solution to ln((ab^3)/(sqrt(cd^3))) is ln(a)+3ln(b)-ln(sqrt(c)sqrt(d)sqrt(d^2))

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simplify ln((ab^3)/(sqrt(cd^3)))

simplify

ln (\frac{a b ^{3}}{c d ^{3}})

ln (a) + 3 ln (b) - ln (c d d^{2})

Solution steps

ln (\frac{a b ^{3}}{c d ^{3}})

Apply log rule:

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

ln (\frac{a b ^{3}}{c d ^{3}}) = ln (a b^{3}) - ln (c d^{3})

= ln (a b^{3}) - ln (c d^{3})

Apply log rule:

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

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

= ln (a) + ln (b^{3}) - ln (c d^{3})

Apply log rule:

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

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

= ln (a) + 3 ln (b) - ln (c d^{3})

c d^{3} = c d d^{2}

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

lo g_{0.4} (\frac{3}{2}) - lo g_{2.5} (2)

lo g_{10} (\frac{z ^{4}}{x ^{5} y})

lo g_{2} (\frac{4}{y}) 5

lo g_{10} (\frac{u ^{2} + v ^{2}}{10000})

- lo g_{10} (2.3 \cdot 1 0^{- 5})

What is ln((ab^3)/(sqrt(cd^3))) ?
The solution to ln((ab^3)/(sqrt(cd^3))) is ln(a)+3ln(b)-ln(sqrt(c)sqrt(d)sqrt(d^2))