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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

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

- lo g_{10} (1.07 \cdot 1 0^{- 6})

- lo g_{10} (1.47 x 1 0^{- 150})

ln (\frac{x}{14})

ln (\frac{5 x - 2 - x sin ( \frac{π x}{2} )}{x ^{2} - 4 x + 6})

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