What is log_{10}(a)+3log_{10}(2b) ?

The solution to log_{10}(a)+3log_{10}(2b) is log_{10}(8ab^3)

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simplify log_{10}(a)+3log_{10}(2b)

simplify

lo g_{10} (a) + 3 lo g_{10} (2 b)

lo g_{10} (8 a b^{3})

Solution steps

lo g_{10} (a) + 3 lo g_{10} (2 b)

Apply log rule:

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

3 lo g_{10} (2 b) = lo g_{10} ((2 b)^{3})

= lo g_{10} (a) + lo g_{10} ((2 b)^{3})

Apply log rule:

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

lo g_{10} (a) + lo g_{10} ((2 b)^{3}) = lo g_{10} (a (2 b)^{3})

= lo g_{10} (a (2 b)^{3})

Simplify

(2 b)^{3} : 8 b^{3}

= lo g_{10} (a \cdot 8 b^{3})

= lo g_{10} (8 a b^{3})

ln (\frac{4}{e})

lo g_{4} (4 x^{2})

lo g_{b} (4 x) + 7 (lo g_{b} (x) - lo g_{b} (y))

\frac{1}{3} \cdot lo g_{4} (8) + lo g_{4} (15)

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

What is log_{10}(a)+3log_{10}(2b) ?
The solution to log_{10}(a)+3log_{10}(2b) is log_{10}(8ab^3)