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

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

Popular >

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Simplify

lo g_{10} (y^{2} z) : 2 lo g_{10} (y) + lo g_{10} (z)

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

Apply the distributive law:

- (a + b) = - a - b

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

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

2 lo g_{2} (3) - 5 lo g_{2} (x) + 2 lo g_{2} (4)

ln (c) - ln (d) + ln (0.017 + c) - ln (0.017 - d)

ln (\frac{x ( x ^{6} + 23 )}{x ^{3} + x - 2})

lo g_{b} (\frac{3 x ^{2}}{b ^{2}})

lo g_{4} (\frac{y ^{8}}{16 x})

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