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

The solution to log_{10}(z)+3log_{10}(y) is log_{10}(zy^3)

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simplify log_{10}(z)+3log_{10}(y)

simplify

lo g_{10} (z) + 3 lo g_{10} (y)

lo g_{10} (z y^{3})

Solution steps

lo g_{10} (z) + 3 lo g_{10} (y)

Apply log rule:

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

3 lo g_{10} (y) = lo g_{10} (y^{3})

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

Apply log rule:

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

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

= lo g_{10} (z y^{3})

- lo g_{10} (1 x 1 0^{- 8})

c^{x} - ln (c^{x}) + ln (x)

ln (\frac{c}{e ^{4 x}})

ln (\frac{c - x}{c + y})

\frac{1}{2} ln (17)

What is log_{10}(z)+3log_{10}(y) ?
The solution to log_{10}(z)+3log_{10}(y) is log_{10}(zy^3)