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}})

ln (\frac{1}{a})

lo g_{a} (x) - lo g_{a} (\frac{1}{x})

lo g_{2} (\frac{x}{2})

e^{x} - ln (4 e^{e^{x}})

ln (10) - ln (5)

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))