What is log_{10}((10z)/4) ?

The solution to log_{10}((10z)/4) is log_{10}(5)+log_{10}(z)-log_{10}(2)

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simplify log_{10}((10z)/4)

simplify

lo g_{10} (\frac{10 z}{4})

lo g_{10} (5) + lo g_{10} (z) - lo g_{10} (2)

Solution steps

lo g_{10} (\frac{10 z}{4})

Cancel

\frac{10 z}{4} : \frac{5 z}{2}

= lo g_{10} (\frac{5 z}{2})

Apply log rule:

lo g_{a} (\frac{x}{y}) = lo g_{a} (x) - lo g_{a} (y)

lo g_{10} (\frac{5 z}{2}) = lo g_{10} (5 z) - lo g_{10} (2)

= lo g_{10} (5 z) - lo g_{10} (2)

Simplify

lo g_{10} (5 z) : lo g_{10} (5) + lo g_{10} (z)

= lo g_{10} (5) + lo g_{10} (z) - lo g_{10} (2)

lo g_{7} (\frac{c}{49})

lo g_{10} (\frac{a ^{2} b ^{\frac{1}{3}}}{c ^{4}})

10 ln (x^{2} y^{5} z^{3}) - λ (5 x + 2 y + 8 z)

lo g_{10} (y x^{5})

7 lo g_{3} (u) + 4 lo g_{3} (v)

What is log_{10}((10z)/4) ?
The solution to log_{10}((10z)/4) is log_{10}(5)+log_{10}(z)-log_{10}(2)