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

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

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

simplify

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

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

Solution steps

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Multiply fractions:

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

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

lo g_{10} (2 x)

lo g_{3} (2 x)

3 lo g_{b} (b) + lo g_{b} (b^{2}) + lo g_{b} (b^{- 5})

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

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

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