What is log_{10}(y)+12log_{10}(z) ?

The solution to log_{10}(y)+12log_{10}(z) is log_{10}(yz^{12})

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simplify log_{10}(y)+12log_{10}(z)

simplify

lo g_{10} (y) + 12 lo g_{10} (z)

lo g_{10} (y z^{12})

Solution steps

lo g_{10} (y) + 12 lo g_{10} (z)

Apply log rule:

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

12 lo g_{10} (z) = lo g_{10} (z^{12})

= lo g_{10} (y) + lo g_{10} (z^{12})

Apply log rule:

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

lo g_{10} (y) + lo g_{10} (z^{12}) = lo g_{10} (y z^{12})

= lo g_{10} (y z^{12})

lo g_{2} (\frac{x}{8})

lo g_{2} (2 x)

lo g_{10} (\frac{y}{100000})

3 lo g_{b} (x) + lo g_{b} (2 x + 1)

4 lo g_{3} (2 x - 1) - \frac{1}{2} lo g_{3} ((x + 1)^{2})

What is log_{10}(y)+12log_{10}(z) ?
The solution to log_{10}(y)+12log_{10}(z) is log_{10}(yz^{12})