What is 2log_{10}(x)+6log_{10}(x+4) ?

The solution to 2log_{10}(x)+6log_{10}(x+4) is log_{10}(x^2(x+4)^6)

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simplify 2log_{10}(x)+6log_{10}(x+4)

simplify

2 lo g_{10} (x) + 6 lo g_{10} (x + 4)

lo g_{10} (x^{2} (x + 4)^{6})

Solution steps

2 lo g_{10} (x) + 6 lo g_{10} (x + 4)

Apply log rule:

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

2 lo g_{10} (x) = lo g_{10} (x^{2})

= lo g_{10} (x^{2}) + 6 lo g_{10} (x + 4)

Apply log rule:

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

6 lo g_{10} (x + 4) = lo g_{10} ((x + 4)^{6})

= lo g_{10} (x^{2}) + lo g_{10} ((x + 4)^{6})

Apply log rule:

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

lo g_{10} (x^{2}) + lo g_{10} ((x + 4)^{6}) = lo g_{10} (x^{2} (x + 4)^{6})

= lo g_{10} (x^{2} (x + 4)^{6})

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

lo g_{10} (2 \cdot 1 0^{- 7})

ln (2) + 3 ln (3)

ln (4) + \frac{1}{2} ln (9)

What is 2log_{10}(x)+6log_{10}(x+4) ?
The solution to 2log_{10}(x)+6log_{10}(x+4) is log_{10}(x^2(x+4)^6)