What is log_{a}((sqrt(x))/(y^8z)) ?

The solution to log_{a}((sqrt(x))/(y^8z)) is log_{a}(sqrt(x))-8log_{a}(y)-log_{a}(z)

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simplify log_{a}((sqrt(x))/(y^8z))

simplify

lo g_{a} (\frac{x}{y ^{8} z})

lo g_{a} (x) - 8 lo g_{a} (y) - lo g_{a} (z)

Solution steps

lo g_{a} (\frac{x}{y ^{8} z})

Apply log rule:

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

lo g_{a} (\frac{x}{y ^{8} z}) = lo g_{a} (x) - lo g_{a} (y^{8} z)

= lo g_{a} (x) - lo g_{a} (y^{8} z)

Simplify

lo g_{a} (y^{8} z) : 8 lo g_{a} (y) + lo g_{a} (z)

= lo g_{a} (x) - (8 lo g_{a} (y) + lo g_{a} (z))

Apply the distributive law:

- (a + b) = - a - b

- (8 lo g_{a} (y) + lo g_{a} (z)) = - 8 lo g_{a} (y) - lo g_{a} (z)

= lo g_{a} (x) - 8 lo g_{a} (y) - lo g_{a} (z)

2 lo g_{10} (a) + 4 lo g_{10} (b) - 9 lo g_{10} (c)

\frac{1}{2} [5 ln (x + 4) + ln (x) - ln (x^{5} - 3)]

ln (24) - ln (6)

\frac{1}{2} (lo g_{9} (a) + lo g_{9} (b))

2 lo g_{10} (x) + lo g_{10} (6) - lo g_{10} (30)

What is log_{a}((sqrt(x))/(y^8z)) ?
The solution to log_{a}((sqrt(x))/(y^8z)) is log_{a}(sqrt(x))-8log_{a}(y)-log_{a}(z)