What is log_{10}(x)-2log_{10}(y)+log_{10}(z) ?

The solution to log_{10}(x)-2log_{10}(y)+log_{10}(z) is log_{10}((xz)/(y^2))

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simplify log_{10}(x)-2log_{10}(y)+log_{10}(z)

simplify

lo g_{10} (x) - 2 lo g_{10} (y) + lo g_{10} (z)

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

Solution steps

lo g_{10} (x) - 2 lo g_{10} (y) + lo g_{10} (z)

Apply log rule:

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

2 lo g_{10} (y) = lo g_{10} (y^{2})

= lo g_{10} (x) - lo g_{10} (y^{2}) + lo g_{10} (z)

Apply log rule:

lo g_{c} (a) - lo g_{c} (b) = lo g_{c} (\frac{a}{b})

lo g_{10} (x) - lo g_{10} (y^{2}) = lo g_{10} (\frac{x}{y ^{2}})

= lo g_{10} (\frac{x}{y ^{2}}) + lo g_{10} (z)

Apply log rule:

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

lo g_{10} (\frac{x}{y ^{2}}) + lo g_{10} (z) = lo g_{10} (\frac{x}{y ^{2}} z)

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

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

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

ln (\frac{40}{80})

3 lo g_{6} (x) + 2 lo g_{6} (y) - \frac{1}{2} lo g_{6} (z)

- lo g_{10} (6.4 \cdot 1 0^{- 10})

- \frac{1}{2} + \frac{1}{2} ln (\frac{4 + 7}{3})

- \frac{ln ( \frac{45}{203} )}{ln ( \frac{293}{313} ) - ln ( \frac{45}{203} )}

What is log_{10}(x)-2log_{10}(y)+log_{10}(z) ?
The solution to log_{10}(x)-2log_{10}(y)+log_{10}(z) is log_{10}((xz)/(y^2))