What is 2log_{10}(x)-4log_{10}(y)+3log_{10}(z) ?

The solution to 2log_{10}(x)-4log_{10}(y)+3log_{10}(z) is log_{10}((x^2z^3)/(y^4))

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simplify 2log_{10}(x)-4log_{10}(y)+3log_{10}(z)

simplify

2 lo g_{10} (x) - 4 lo g_{10} (y) + 3 lo g_{10} (z)

lo g_{10} (\frac{x ^{2} z ^{3}}{y ^{4}})

Solution steps

2 lo g_{10} (x) - 4 lo g_{10} (y) + 3 lo g_{10} (z)

Apply log rule:

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

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

= lo g_{10} (x^{2}) - 4 lo g_{10} (y) + 3 lo g_{10} (z)

Apply log rule:

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

4 lo g_{10} (y) = lo g_{10} (y^{4})

= lo g_{10} (x^{2}) - lo g_{10} (y^{4}) + 3 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^{2}) - lo g_{10} (y^{4}) = lo g_{10} (\frac{x ^{2}}{y ^{4}})

= lo g_{10} (\frac{x ^{2}}{y ^{4}}) + 3 lo g_{10} (z)

Apply log rule:

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

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

= lo g_{10} (\frac{x ^{2}}{y ^{4}}) + lo g_{10} (z^{3})

Apply log rule:

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

lo g_{10} (\frac{x ^{2}}{y ^{4}}) + lo g_{10} (z^{3}) = lo g_{10} (\frac{x ^{2}}{y ^{4}} z^{3})

= lo g_{10} (\frac{x ^{2}}{y ^{4}} z^{3})

Multiply fractions:

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

= lo g_{10} (\frac{x ^{2} z ^{3}}{y ^{4}})

- lo g_{10} (1.8 \cdot 1 0^{- 5})

lo g_{10} (\frac{10 a 0.1}{10})

- lo g_{10} (4.1 \cdot 1 0^{- 3})

4 lo g_{10} (3 x^{3}) - \frac{1}{2} lo g_{10} (9 x^{8})

lo g_{10} (81) - lo g_{10} (\frac{64}{36})

What is 2log_{10}(x)-4log_{10}(y)+3log_{10}(z) ?
The solution to 2log_{10}(x)-4log_{10}(y)+3log_{10}(z) is log_{10}((x^2z^3)/(y^4))