What is ln((sqrt(a))/(b^3)) ?

The solution to ln((sqrt(a))/(b^3)) is ln(sqrt(a))-3ln(b)

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simplify ln((sqrt(a))/(b^3))

simplify

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

ln (a) - 3 ln (b)

Solution steps

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

Apply log rule:

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

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

= ln (a) - ln (b^{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)

lo g_{10} (\frac{π}{2})

ln (\frac{( w ^{3} )}{z})

ln (2 x) - 2 ln (y) + ln (z)

ln (\frac{5 x}{y ^{2}})

ln (y) - ln (c) - ln (x)

What is ln((sqrt(a))/(b^3)) ?
The solution to ln((sqrt(a))/(b^3)) is ln(sqrt(a))-3ln(b)