What is log_{10}(y)+13log_{10}(z) ?

The solution to log_{10}(y)+13log_{10}(z) is log_{10}(yz^{13})

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simplify log_{10}(y)+13log_{10}(z)

simplify

lo g_{10} (y) + 13 lo g_{10} (z)

lo g_{10} (y z^{13})

Solution steps

lo g_{10} (y) + 13 lo g_{10} (z)

Apply log rule:

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

13 lo g_{10} (z) = lo g_{10} (z^{13})

= lo g_{10} (y) + lo g_{10} (z^{13})

Apply log rule:

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

lo g_{10} (y) + lo g_{10} (z^{13}) = lo g_{10} (y z^{13})

= lo g_{10} (y z^{13})

4 lo g_{6} (y) - \frac{1}{4} lo g_{6} (z)

lo g_{10} (2) + lo g_{10} (8) - lo g_{10} (4)

lo g_{10} (\frac{x}{2})

lo g_{10} (\frac{z ^{3}}{x ^{5} y})

lo g_{10} (\frac{3 x ^{5}}{y ^{2} z})

What is log_{10}(y)+13log_{10}(z) ?
The solution to log_{10}(y)+13log_{10}(z) is log_{10}(yz^{13})