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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

f (z) = lo g_{10} (\frac{10 z}{9})

ln (\frac{x ^{2} y ^{3}}{z ^{5}})

lo g_{5} (60) - lo g_{5} (50) + lo g_{5} (30)

ln (\frac{y}{1 - y})

ln (\frac{358.15}{295.15})

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