What is 2log_{3}(k)-5log_{3}(m)+log_{3}(n+3) ?

The solution to 2log_{3}(k)-5log_{3}(m)+log_{3}(n+3) is log_{3}((k^2(n+3))/(m^5))

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simplify 2log_{3}(k)-5log_{3}(m)+log_{3}(n+3)

simplify

2 lo g_{3} (k) - 5 lo g_{3} (m) + lo g_{3} (n + 3)

lo g_{3} (\frac{k ^{2} ( n + 3 )}{m ^{5}})

Solution steps

2 lo g_{3} (k) - 5 lo g_{3} (m) + lo g_{3} (n + 3)

Apply log rule:

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

2 lo g_{3} (k) = lo g_{3} (k^{2})

= lo g_{3} (k^{2}) - 5 lo g_{3} (m) + lo g_{3} (n + 3)

Apply log rule:

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

5 lo g_{3} (m) = lo g_{3} (m^{5})

= lo g_{3} (k^{2}) - lo g_{3} (m^{5}) + lo g_{3} (n + 3)

Apply log rule:

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

lo g_{3} (k^{2}) - lo g_{3} (m^{5}) = lo g_{3} (\frac{k ^{2}}{m ^{5}})

= lo g_{3} (\frac{k ^{2}}{m ^{5}}) + lo g_{3} (n + 3)

Apply log rule:

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

lo g_{3} (\frac{k ^{2}}{m ^{5}}) + lo g_{3} (n + 3) = lo g_{3} (\frac{k ^{2}}{m ^{5}} (n + 3))

= lo g_{3} (\frac{k ^{2}}{m ^{5}} (n + 3))

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= lo g_{3} (\frac{k ^{2} ( n + 3 )}{m ^{5}})

lo g_{3} (2 x - 3) - lo g_{3} (x + 6)

lo g_{4} (6) + 2 lo g_{4} (x)

ln (\frac{21}{8})

ln (\frac{x ^{4} y ^{5}}{z ^{3}})

lo g_{7} (10) - lo g_{7} (3) - 4 lo g_{7} (x)

What is 2log_{3}(k)-5log_{3}(m)+log_{3}(n+3) ?
The solution to 2log_{3}(k)-5log_{3}(m)+log_{3}(n+3) is log_{3}((k^2(n+3))/(m^5))