What is log_{10}(x)+6log_{10}(x+7) ?

The solution to log_{10}(x)+6log_{10}(x+7) is log_{10}(x(x+7)^6)

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simplify log_{10}(x)+6log_{10}(x+7)

simplify

lo g_{10} (x) + 6 lo g_{10} (x + 7)

lo g_{10} (x (x + 7)^{6})

Solution steps

lo g_{10} (x) + 6 lo g_{10} (x + 7)

Apply log rule:

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

6 lo g_{10} (x + 7) = lo g_{10} ((x + 7)^{6})

= lo g_{10} (x) + lo g_{10} ((x + 7)^{6})

Apply log rule:

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

lo g_{10} (x) + lo g_{10} ((x + 7)^{6}) = lo g_{10} (x (x + 7)^{6})

= lo g_{10} (x (x + 7)^{6})

lo g_{10} (0.401) - lo g_{10} (0.8)

lo g_{4} (7 x y)

7 (lo g_{4} (3) + lo g_{4} (y)) - lo g_{4} (2)

lo g_{10} (\frac{x}{y ^{7}})

lo g_{10} (1.54 x) lo g_{10} (1.02)

What is log_{10}(x)+6log_{10}(x+7) ?
The solution to log_{10}(x)+6log_{10}(x+7) is log_{10}(x(x+7)^6)