What is 2ln(a^2)-3ln(b) ?

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

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simplify 2ln(a^2)-3ln(b)

simplify

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

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

Solution steps

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

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

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

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

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

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

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

Apply log rule:

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

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

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

(a^{2})^{2} = a^{4}

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

lo g_{10} (x + 2) + 2 lo g_{10} (x - 3)

lo g_{10} (\frac{k ^{3}}{2})

lo g_{10} (\frac{24 m ^{2}}{16 p})

ln (ln (a + b) + ln (a - b) - 8 ln (c))