What is log_{10}(3z)+2log_{10}(7) ?

The solution to log_{10}(3z)+2log_{10}(7) is log_{10}(147z)

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simplify log_{10}(3z)+2log_{10}(7)

simplify

lo g_{10} (3 z) + 2 lo g_{10} (7)

lo g_{10} (147 z)

Solution steps

lo g_{10} (3 z) + 2 lo g_{10} (7)

Apply log rule:

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

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

= lo g_{10} (3 z) + lo g_{10} (7^{2})

Apply log rule:

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

lo g_{10} (3 z) + lo g_{10} (7^{2}) = lo g_{10} (3 z \cdot 7^{2})

= lo g_{10} (3 z \cdot 7^{2})

Simplify

3 z \cdot 7^{2} : 147 z

= lo g_{10} (147 z)

\frac{1}{2} ln (\frac{x - 1}{x + 1})

lo g_{10} (2 x) + 3 lo g_{10} (2 y)

lo g_{10} (p) - \frac{1}{3} lo g_{10} (q)

ln (5) + \frac{1}{2} ln (9)

lo g_{6} (\frac{x ^{3}}{y ^{8}})

What is log_{10}(3z)+2log_{10}(7) ?
The solution to log_{10}(3z)+2log_{10}(7) is log_{10}(147z)