What is log_{10}(((x^2))/((y^4*sqrt(z)))) ?

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

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simplify log_{10}(((x^2))/((y^4*sqrt(z))))

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

lo g_{10} (x^{2}) = 2 lo g_{10} (x)

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

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

Apply the distributive law:

- (a + b) = - a - b

- (4 lo g_{10} (y) + lo g_{10} (z)) = - 4 lo g_{10} (y) - lo g_{10} (z)

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

ln (21 x^{3.4})

- lo g_{10} (6.68 \cdot 1 0^{- 2})

lo g_{9} (\frac{w ^{4}}{v})

ln (3^{b} a^{b})

2 lo g_{4} (y - 1) - lo g_{4} (y + 3) - 1

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