What is log_{5}((sqrt(x))/(3^2z)) ?

The solution to log_{5}((sqrt(x))/(3^2z)) is log_{5}(sqrt(x))-2log_{5}(3)-log_{5}(z)

Popular >

simplify log_{5}((sqrt(x))/(3^2z))

simplify

lo g_{5} (\frac{x}{3 ^{2} z})

lo g_{5} (x) - 2 lo g_{5} (3) - lo g_{5} (z)

Solution steps

lo g_{5} (\frac{x}{3 ^{2} z})

Simplify

\frac{x}{3 ^{2} z} : \frac{x}{9 z}

= lo g_{5} (\frac{x}{9 z})

Apply log rule:

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

lo g_{5} (\frac{x}{9 z}) = lo g_{5} (x) - lo g_{5} (9 z)

= lo g_{5} (x) - lo g_{5} (9 z)

Simplify

lo g_{5} (9 z) : 2 lo g_{5} (3) + lo g_{5} (z)

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

Apply the distributive law:

- (a + b) = - a - b

- (2 lo g_{5} (3) + lo g_{5} (z)) = - 2 lo g_{5} (3) - lo g_{5} (z)

= lo g_{5} (x) - 2 lo g_{5} (3) - lo g_{5} (z)

3.8 + lo g_{10} (\frac{0.18}{0.52})

lo g_{10} (\frac{y ^{9}}{2 x})

ln (\frac{7}{5 x ^{5} y})

3 lo g_{10} (x + 1) + lo g_{10} (4 x + 7)

lo g_{10} (\frac{7 a}{8})

What is log_{5}((sqrt(x))/(3^2z)) ?
The solution to log_{5}((sqrt(x))/(3^2z)) is log_{5}(sqrt(x))-2log_{5}(3)-log_{5}(z)