What is 8log_{10}(x)-7log_{10}(x+1) ?

The solution to 8log_{10}(x)-7log_{10}(x+1) is log_{10}((x^8)/((x+1)^7))

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simplify 8log_{10}(x)-7log_{10}(x+1)

simplify

8 lo g_{10} (x) - 7 lo g_{10} (x + 1)

lo g_{10} (\frac{x ^{8}}{( x + 1 ) ^{7}})

Solution steps

8 lo g_{10} (x) - 7 lo g_{10} (x + 1)

Apply log rule:

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

8 lo g_{10} (x) = lo g_{10} (x^{8})

= lo g_{10} (x^{8}) - 7 lo g_{10} (x + 1)

Apply log rule:

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

7 lo g_{10} (x + 1) = lo g_{10} ((x + 1)^{7})

= lo g_{10} (x^{8}) - lo g_{10} ((x + 1)^{7})

Apply log rule:

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

lo g_{10} (x^{8}) - lo g_{10} ((x + 1)^{7}) = lo g_{10} (\frac{x ^{8}}{( x + 1 ) ^{7}})

= lo g_{10} (\frac{x ^{8}}{( x + 1 ) ^{7}})

lo g_{4} (10) + lo g_{4} (7) + 4 lo g_{4} (3)

lo g_{10} (x) + lo g_{10} (4)

lo g_{2} (\frac{π - 0.1}{1 0 ^{- 6}})

lo g_{b} (7 x \cdot 2 y)

1 - lo g_{\frac{1}{3}} (x) + lo g_{\frac{1}{3}} (x + 3)

What is 8log_{10}(x)-7log_{10}(x+1) ?
The solution to 8log_{10}(x)-7log_{10}(x+1) is log_{10}((x^8)/((x+1)^7))