What is 2log_{m}(x-3)-4log_{m}(x+4) ?

The solution to 2log_{m}(x-3)-4log_{m}(x+4) is log_{m}(((x-3)^2)/((x+4)^4))

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simplify 2log_{m}(x-3)-4log_{m}(x+4)

simplify

2 lo g_{m} (x - 3) - 4 lo g_{m} (x + 4)

lo g_{m} (\frac{( x - 3 ) ^{2}}{( x + 4 ) ^{4}})

Solution steps

2 lo g_{m} (x - 3) - 4 lo g_{m} (x + 4)

Apply log rule:

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

2 lo g_{m} (x - 3) = lo g_{m} ((x - 3)^{2})

= lo g_{m} ((x - 3)^{2}) - 4 lo g_{m} (x + 4)

Apply log rule:

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

4 lo g_{m} (x + 4) = lo g_{m} ((x + 4)^{4})

= lo g_{m} ((x - 3)^{2}) - lo g_{m} ((x + 4)^{4})

Apply log rule:

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

lo g_{m} ((x - 3)^{2}) - lo g_{m} ((x + 4)^{4}) = lo g_{m} (\frac{( x - 3 ) ^{2}}{( x + 4 ) ^{4}})

= lo g_{m} (\frac{( x - 3 ) ^{2}}{( x + 4 ) ^{4}})

ln (\frac{( - 6 e ^{5 x} )}{5})

- ln (\frac{w}{t})

(ln (50) - ln (12)) \cdot 600

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What is 2log_{m}(x-3)-4log_{m}(x+4) ?
The solution to 2log_{m}(x-3)-4log_{m}(x+4) is log_{m}(((x-3)^2)/((x+4)^4))