What is 6log_{4}(y-5)-5log_{4}(y+4) ?

The solution to 6log_{4}(y-5)-5log_{4}(y+4) is log_{4}(((y-5)^6)/((y+4)^5))

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simplify 6log_{4}(y-5)-5log_{4}(y+4)

simplify

6 lo g_{4} (y - 5) - 5 lo g_{4} (y + 4)

lo g_{4} (\frac{( y - 5 ) ^{6}}{( y + 4 ) ^{5}})

Solution steps

6 lo g_{4} (y - 5) - 5 lo g_{4} (y + 4)

Apply log rule:

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

6 lo g_{4} (y - 5) = lo g_{4} ((y - 5)^{6})

= lo g_{4} ((y - 5)^{6}) - 5 lo g_{4} (y + 4)

Apply log rule:

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

5 lo g_{4} (y + 4) = lo g_{4} ((y + 4)^{5})

= lo g_{4} ((y - 5)^{6}) - lo g_{4} ((y + 4)^{5})

Apply log rule:

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

lo g_{4} ((y - 5)^{6}) - lo g_{4} ((y + 4)^{5}) = lo g_{4} (\frac{( y - 5 ) ^{6}}{( y + 4 ) ^{5}})

= lo g_{4} (\frac{( y - 5 ) ^{6}}{( y + 4 ) ^{5}})

6 lo g_{b} (w) - \frac{1}{5} lo g_{b} (z) + 5 lo g_{b} (x)

- lo g_{10} (5.33 x 1 0^{3})

2 (ln (7) - 3 ln (2))

ln (1 - x) - ln (1 + x)

ln (β \cdot γ^{α X})

What is 6log_{4}(y-5)-5log_{4}(y+4) ?
The solution to 6log_{4}(y-5)-5log_{4}(y+4) is log_{4}(((y-5)^6)/((y+4)^5))