What is 4log_{10}(x)+2log_{10}(y)-5log_{10}(z) ?

The solution to 4log_{10}(x)+2log_{10}(y)-5log_{10}(z) is log_{10}((x^4y^2)/(z^5))

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simplify 4log_{10}(x)+2log_{10}(y)-5log_{10}(z)

simplify

4 lo g_{10} (x) + 2 lo g_{10} (y) - 5 lo g_{10} (z)

lo g_{10} (\frac{x ^{4} y ^{2}}{z ^{5}})

Solution steps

4 lo g_{10} (x) + 2 lo g_{10} (y) - 5 lo g_{10} (z)

Apply log rule:

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

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

= lo g_{10} (x^{4}) + 2 lo g_{10} (y) - 5 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^{4}) + lo g_{10} (y^{2}) - 5 lo g_{10} (z)

Apply log rule:

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

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

= lo g_{10} (x^{4} y^{2}) - 5 lo g_{10} (z)

Apply log rule:

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

5 lo g_{10} (z) = lo g_{10} (z^{5})

= lo g_{10} (x^{4} y^{2}) - lo g_{10} (z^{5})

Apply log rule:

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

lo g_{10} (x^{4} y^{2}) - lo g_{10} (z^{5}) = lo g_{10} (\frac{x ^{4} y ^{2}}{z ^{5}})

= lo g_{10} (\frac{x ^{4} y ^{2}}{z ^{5}})

e^{- l n (l n (x)) - l n (x)}

\frac{1}{4} ln (6 b a^{2}) - ln (m) - \frac{1}{4} ln (5)

- lo g_{10} (2.19 \cdot 1 0^{- 6})

ln (1 - x) - ln (1 - y)

0 ln (\frac{500}{z})

What is 4log_{10}(x)+2log_{10}(y)-5log_{10}(z) ?
The solution to 4log_{10}(x)+2log_{10}(y)-5log_{10}(z) is log_{10}((x^4y^2)/(z^5))