What is log_{8}((x-5)^6(x+7)^2) ?

The solution to log_{8}((x-5)^6(x+7)^2) is 6log_{8}(x-5)+2log_{8}(x+7)

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simplify log_{8}((x-5)^6(x+7)^2)

simplify

lo g_{8} ((x - 5)^{6} (x + 7)^{2})

6 lo g_{8} (x - 5) + 2 lo g_{8} (x + 7)

Solution steps

lo g_{8} ((x - 5)^{6} (x + 7)^{2})

Apply log rule:

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

lo g_{8} ((x - 5)^{6} (x + 7)^{2}) = lo g_{8} ((x - 5)^{6}) + lo g_{8} ((x + 7)^{2})

= lo g_{8} ((x - 5)^{6}) + lo g_{8} ((x + 7)^{2})

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

lo g_{8} ((x - 5)^{6}) = 6 lo g_{8} (x - 5)

= 6 lo g_{8} (x - 5) + lo g_{8} ((x + 7)^{2})

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

lo g_{8} ((x + 7)^{2}) = 2 lo g_{8} (x + 7)

= 6 lo g_{8} (x - 5) + 2 lo g_{8} (x + 7)

ln (m) - ln (m - n)

lo g_{10} (\frac{( 4 \cdot 1 0 ^{- 7} )}{( 1 \cdot 1 0 ^{- 12} )})

ln (p^{x} (1 - p)^{1 - x})

4 lo g_{10} (x) - 9 lo g_{10} (y)

3 lo g_{a} (x + y) - 2 lo g_{a} (x - y)

What is log_{8}((x-5)^6(x+7)^2) ?
The solution to log_{8}((x-5)^6(x+7)^2) is 6log_{8}(x-5)+2log_{8}(x+7)