What is 3log_{10}(x)+6log_{10}(x+8) ?

The solution to 3log_{10}(x)+6log_{10}(x+8) is log_{10}(x^3(x+8)^6)

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simplify 3log_{10}(x)+6log_{10}(x+8)

simplify

3 lo g_{10} (x) + 6 lo g_{10} (x + 8)

lo g_{10} (x^{3} (x + 8)^{6})

Solution steps

3 lo g_{10} (x) + 6 lo g_{10} (x + 8)

Apply log rule:

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

3 lo g_{10} (x) = lo g_{10} (x^{3})

= lo g_{10} (x^{3}) + 6 lo g_{10} (x + 8)

Apply log rule:

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

6 lo g_{10} (x + 8) = lo g_{10} ((x + 8)^{6})

= lo g_{10} (x^{3}) + lo g_{10} ((x + 8)^{6})

Apply log rule:

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

lo g_{10} (x^{3}) + lo g_{10} ((x + 8)^{6}) = lo g_{10} (x^{3} (x + 8)^{6})

= lo g_{10} (x^{3} (x + 8)^{6})

(1) ln (\frac{1100}{1400}) - 0.287 ln (\frac{5}{20})

ln (\frac{a ^{x} + b ^{x} + c ^{x}}{3})

ln (\frac{4 + x ^{2}}{x})

lo g_{10} (2 w^{5} - 7 w) + lo g_{10} (w^{- 1})

lo g_{10} (\frac{100}{x ^{2} + y ^{2}})

What is 3log_{10}(x)+6log_{10}(x+8) ?
The solution to 3log_{10}(x)+6log_{10}(x+8) is log_{10}(x^3(x+8)^6)