What is 3log_{2}(x+8)-5log_{2}(x+2) ?

The solution to 3log_{2}(x+8)-5log_{2}(x+2) is log_{2}(((x+8)^3)/((x+2)^5))

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simplify 3log_{2}(x+8)-5log_{2}(x+2)

simplify

3 lo g_{2} (x + 8) - 5 lo g_{2} (x + 2)

lo g_{2} (\frac{( x + 8 ) ^{3}}{( x + 2 ) ^{5}})

Solution steps

3 lo g_{2} (x + 8) - 5 lo g_{2} (x + 2)

Apply log rule:

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

3 lo g_{2} (x + 8) = lo g_{2} ((x + 8)^{3})

= lo g_{2} ((x + 8)^{3}) - 5 lo g_{2} (x + 2)

Apply log rule:

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

5 lo g_{2} (x + 2) = lo g_{2} ((x + 2)^{5})

= lo g_{2} ((x + 8)^{3}) - lo g_{2} ((x + 2)^{5})

Apply log rule:

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

lo g_{2} ((x + 8)^{3}) - lo g_{2} ((x + 2)^{5}) = lo g_{2} (\frac{( x + 8 ) ^{3}}{( x + 2 ) ^{5}})

= lo g_{2} (\frac{( x + 8 ) ^{3}}{( x + 2 ) ^{5}})

- lo g_{10} (6.4 \cdot 1 0^{- 5})

2 lo g_{7} (x) + 3 lo g_{7} (y)

3 ln (x^{2} y) - 21 ln (x y) + 1

- lo g_{10} (4.8 \cdot 1 0^{- 4})

lo g_{2} (2^{5})

What is 3log_{2}(x+8)-5log_{2}(x+2) ?
The solution to 3log_{2}(x+8)-5log_{2}(x+2) is log_{2}(((x+8)^3)/((x+2)^5))