What is 4log_{10}(x)-2log_{10}(x-3) ?

The solution to 4log_{10}(x)-2log_{10}(x-3) is log_{10}((x^4)/((x-3)^2))

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simplify 4log_{10}(x)-2log_{10}(x-3)

simplify

4 lo g_{10} (x) - 2 lo g_{10} (x - 3)

lo g_{10} (\frac{x ^{4}}{( x - 3 ) ^{2}})

Solution steps

4 lo g_{10} (x) - 2 lo g_{10} (x - 3)

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}) - 2 lo g_{10} (x - 3)

Apply log rule:

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

2 lo g_{10} (x - 3) = lo g_{10} ((x - 3)^{2})

= lo g_{10} (x^{4}) - lo g_{10} ((x - 3)^{2})

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 - 3)^{2}) = lo g_{10} (\frac{x ^{4}}{( x - 3 ) ^{2}})

= lo g_{10} (\frac{x ^{4}}{( x - 3 ) ^{2}})

lo g_{2} (r^{\frac{1}{3}}) t

- lo g_{10} (1.9 \cdot 1 0^{- 3})

lo g_{5} (x^{5})

ln (\frac{1}{x ^{2} + y ^{2}})

\frac{8.314 \cdot 310}{1 \cdot 96485} ln (\frac{5.3}{140})

What is 4log_{10}(x)-2log_{10}(x-3) ?
The solution to 4log_{10}(x)-2log_{10}(x-3) is log_{10}((x^4)/((x-3)^2))