What is 5log_{10}(x+3)-log_{10}(x) ?

The solution to 5log_{10}(x+3)-log_{10}(x) is log_{10}(((x+3)^5)/x)

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simplify 5log_{10}(x+3)-log_{10}(x)

simplify

5 lo g_{10} (x + 3) - lo g_{10} (x)

lo g_{10} (\frac{( x + 3 ) ^{5}}{x})

Solution steps

5 lo g_{10} (x + 3) - lo g_{10} (x)

Apply log rule:

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

5 lo g_{10} (x + 3) = lo g_{10} ((x + 3)^{5})

= lo g_{10} ((x + 3)^{5}) - 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 + 3)^{5}) - lo g_{10} (x) = lo g_{10} (\frac{( x + 3 ) ^{5}}{x})

= lo g_{10} (\frac{( x + 3 ) ^{5}}{x})

lo g_{10} (p^{20} \cdot q^{30} \cdot (1 - p - q)^{50})

lo g_{10} (\frac{m}{n})

lo g_{2} (x) + lo g_{2} (7)

lo g_{5} (x) - lo g_{5} (x^{7})

lo g_{a} (m) + lo g_{a} (n) - lo g_{a} (p)

What is 5log_{10}(x+3)-log_{10}(x) ?
The solution to 5log_{10}(x+3)-log_{10}(x) is log_{10}(((x+3)^5)/x)