What is log_{10}((10z)/9) ?

The solution to log_{10}((10z)/9) is 1+log_{10}(z)-2log_{10}(3)

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simplify log_{10}((10z)/9)

simplify

lo g_{10} (\frac{10 z}{9})

1 + lo g_{10} (z) - 2 lo g_{10} (3)

Solution steps

lo g_{10} (\frac{10 z}{9})

Apply log rule:

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

lo g_{10} (\frac{10 z}{9}) = lo g_{10} (10 z) - lo g_{10} (9)

= lo g_{10} (10 z) - lo g_{10} (9)

lo g_{10} (10 z) = 1 + lo g_{10} (z)

lo g_{10} (9) = 2 lo g_{10} (3)

= 1 + lo g_{10} (z) - 2 lo g_{10} (3)

ln (\frac{x ^{2} y ^{3}}{z ^{5}})

lo g_{5} (60) - lo g_{5} (50) + lo g_{5} (30)

ln (\frac{y}{1 - y})

ln (\frac{358.15}{295.15})

lo g_{b} (\frac{b}{c}) + lo g_{b} (b c)

What is log_{10}((10z)/9) ?
The solution to log_{10}((10z)/9) is 1+log_{10}(z)-2log_{10}(3)