What is 5log_{10}(x)-2log_{10}(x+7) ?

The solution to 5log_{10}(x)-2log_{10}(x+7) is log_{10}((x^5)/((x+7)^2))

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simplify 5log_{10}(x)-2log_{10}(x+7)

simplify

5 lo g_{10} (x) - 2 lo g_{10} (x + 7)

lo g_{10} (\frac{x ^{5}}{( x + 7 ) ^{2}})

Solution steps

5 lo g_{10} (x) - 2 lo g_{10} (x + 7)

Apply log rule:

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

5 lo g_{10} (x) = lo g_{10} (x^{5})

= lo g_{10} (x^{5}) - 2 lo g_{10} (x + 7)

Apply log rule:

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

2 lo g_{10} (x + 7) = lo g_{10} ((x + 7)^{2})

= lo g_{10} (x^{5}) - lo g_{10} ((x + 7)^{2})

Apply log rule:

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

lo g_{10} (x^{5}) - lo g_{10} ((x + 7)^{2}) = lo g_{10} (\frac{x ^{5}}{( x + 7 ) ^{2}})

= lo g_{10} (\frac{x ^{5}}{( x + 7 ) ^{2}})

lo g_{10} (\frac{x ^{2} y ^{2}}{z})

lo g_{10} (0.1) + lo g_{10} (0.001)

lo g_{10} (\frac{1000}{p ^{2} + 9})

2 ln (x) - ln (x - y) + 2 ln (y)

8.1 + lo g_{10} (\frac{0.11 + 0.03}{0.18 - 0.03})

What is 5log_{10}(x)-2log_{10}(x+7) ?
The solution to 5log_{10}(x)-2log_{10}(x+7) is log_{10}((x^5)/((x+7)^2))