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

The solution to 4log_{10}(3x)-2log_{10}(y) is log_{10}((81x^4)/(y^2))

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

simplify

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

lo g_{10} (\frac{81 x ^{4}}{y ^{2}})

Solution steps

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

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

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

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

Apply log rule:

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

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

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

Simplify

(3 x)^{4} : 81 x^{4}

= lo g_{10} (\frac{81 x ^{4}}{y ^{2}})

3 ln (x) + 2 ln (y) - 5 ln (z)

4 lo g_{9} (6) - lo g_{9} (3)

lo g_{9} (27) + lo g_{9} (3)

What is 4log_{10}(3x)-2log_{10}(y) ?
The solution to 4log_{10}(3x)-2log_{10}(y) is log_{10}((81x^4)/(y^2))