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

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

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

simplify

4 \cdot lo g_{10} (x) - (2 \cdot lo g_{10} (v) + 3 \cdot lo g_{10} (y))

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

Solution steps

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

Apply the distributive law:

- (a + b) = - a - b

- (2 lo g_{10} (v) + 3 lo g_{10} (y)) = - 2 lo g_{10} (v) - 3 lo g_{10} (y)

= 4 lo g_{10} (x) - 2 lo g_{10} (v) - 3 lo g_{10} (y)

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

- 2 lo g_{10} (v) = - lo g_{10} (v^{2})

- 3 lo g_{10} (y) = - lo g_{10} (y^{3})

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

Apply log rule:

lo g_{a} (x) - lo g_{a} (y) = lo g_{a} (\frac{x}{y})

lo g_{10} (x^{4}) - lo g_{10} (v^{2}) = lo g_{10} (\frac{x ^{4}}{v ^{2}})

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

Apply log rule:

lo g_{a} (x) - lo g_{a} (y) = lo g_{a} (\frac{x}{y})

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

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

Simplify

\frac{\frac{x ^{4}}{v ^{2}}}{y ^{3}} : \frac{x ^{4}}{v ^{2} y ^{3}}

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

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

lo g_{10} (\frac{x + 1}{x ^{2} + 1})

lo g_{10} (x^{\frac{3}{5}} y^{4})

lo g_{10} (x^{3} \cdot y^{- 2})

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