What is log_{10}(p)+2log_{10}(8s) ?

The solution to log_{10}(p)+2log_{10}(8s) is log_{10}(64ps^2)

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simplify log_{10}(p)+2log_{10}(8s)

simplify

lo g_{10} (p) + 2 lo g_{10} (8 s)

lo g_{10} (64 p s^{2})

Solution steps

lo g_{10} (p) + 2 lo g_{10} (8 s)

Apply log rule:

b \cdot lo g_{a} (x) = lo g_{a} (x^{b})

2 lo g_{10} (8 s) = lo g_{10} ((8 s)^{2})

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

Apply log rule:

lo g_{a} (x) + lo g_{a} (y) = lo g_{a} (x y)

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

= lo g_{10} (p (8 s)^{2})

Simplify

(8 s)^{2} : 64 s^{2}

= lo g_{10} (p \cdot 64 s^{2})

= lo g_{10} (64 p s^{2})

ln (x (x - 1))

ln (\frac{3 ^{x} 6 ^{2 x}}{2 ^{3 x}})

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

3 ln (3) + 3 ln (c)

\frac{1}{3} ln (18)

What is log_{10}(p)+2log_{10}(8s) ?
The solution to log_{10}(p)+2log_{10}(8s) is log_{10}(64ps^2)