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

The solution to 2log_{10}(x)+log_{10}(x+2) is log_{10}(x^2(x+2))

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simplify 2log_{10}(x)+log_{10}(x+2)

simplify

2 lo g_{10} (x) + lo g_{10} (x + 2)

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

Solution steps

2 lo g_{10} (x) + lo g_{10} (x + 2)

Apply log rule:

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

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

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

Apply log rule:

lo g_{c} (a) + lo g_{c} (b) = lo g_{c} (ab)

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

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

lo g_{10} (x) - lo g_{10} (y) - lo g_{10} (z)

\frac{1}{3} ln (x) + ln (y)

\frac{1}{8} ln (y) + ln (z)

ln (x yz)

2 ln (x) - 3 ln (y)

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