What is 3log_{10}(x)-2log_{10}(x+8) ?

The solution to 3log_{10}(x)-2log_{10}(x+8) is log_{10}((x^3)/((x+8)^2))

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simplify 3log_{10}(x)-2log_{10}(x+8)

simplify

3 lo g_{10} (x) - 2 lo g_{10} (x + 8)

lo g_{10} (\frac{x ^{3}}{( x + 8 ) ^{2}})

Solution steps

3 lo g_{10} (x) - 2 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}) - 2 lo g_{10} (x + 8)

Apply log rule:

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

2 lo g_{10} (x + 8) = lo g_{10} ((x + 8)^{2})

= lo g_{10} (x^{3}) - lo g_{10} ((x + 8)^{2})

Apply log rule:

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

lo g_{10} (x^{3}) - lo g_{10} ((x + 8)^{2}) = lo g_{10} (\frac{x ^{3}}{( x + 8 ) ^{2}})

= lo g_{10} (\frac{x ^{3}}{( x + 8 ) ^{2}})

ln (\frac{1}{35.2 - 1})

- ln (u) + \frac{1}{2} \cdot ln (u - 1) + \frac{1}{2} \cdot ln (u - 1)

ln (\frac{1}{x ^{6}})

ln (\frac{y cos ( y )}{d y})

- lo g_{10} (3.3333 \cdot 1 0^{- 3})

What is 3log_{10}(x)-2log_{10}(x+8) ?
The solution to 3log_{10}(x)-2log_{10}(x+8) is log_{10}((x^3)/((x+8)^2))