What is 3log_{10}(x)+4log_{10}(y)-6log_{10}(z) ?

The solution to 3log_{10}(x)+4log_{10}(y)-6log_{10}(z) is log_{10}((x^3y^4)/(z^6))

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simplify 3log_{10}(x)+4log_{10}(y)-6log_{10}(z)

simplify

3 lo g_{10} (x) + 4 lo g_{10} (y) - 6 lo g_{10} (z)

lo g_{10} (\frac{x ^{3} y ^{4}}{z ^{6}})

Solution steps

3 lo g_{10} (x) + 4 lo g_{10} (y) - 6 lo g_{10} (z)

Apply log rule:

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

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

= lo g_{10} (x^{3}) + 4 lo g_{10} (y) - 6 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^{3}) + lo g_{10} (y^{4}) - 6 lo g_{10} (z)

Apply log rule:

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

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

= lo g_{10} (x^{3} y^{4}) - 6 lo g_{10} (z)

Apply log rule:

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

6 lo g_{10} (z) = lo g_{10} (z^{6})

= lo g_{10} (x^{3} y^{4}) - lo g_{10} (z^{6})

Apply log rule:

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

lo g_{10} (x^{3} y^{4}) - lo g_{10} (z^{6}) = lo g_{10} (\frac{x ^{3} y ^{4}}{z ^{6}})

= lo g_{10} (\frac{x ^{3} y ^{4}}{z ^{6}})

2 \cdot (ln (0.07) - ln (0.06))

ln (258) - ln (2)

ln (\frac{35 + 150}{738 + 150})

- lo g_{10} (6.6 \cdot 1 0^{- 5})

What is 3log_{10}(x)+4log_{10}(y)-6log_{10}(z) ?
The solution to 3log_{10}(x)+4log_{10}(y)-6log_{10}(z) is log_{10}((x^3y^4)/(z^6))