What is log_{8}((w^4x^2)/(yz)) ?

The solution to log_{8}((w^4x^2)/(yz)) is 4log_{8}(w)+2log_{8}(x)-log_{8}(y)-log_{8}(z)

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simplify log_{8}((w^4x^2)/(yz))

simplify

lo g_{8} (\frac{w ^{4} x ^{2}}{yz})

4 lo g_{8} (w) + 2 lo g_{8} (x) - lo g_{8} (y) - lo g_{8} (z)

Solution steps

lo g_{8} (\frac{w ^{4} x ^{2}}{yz})

Apply log rule:

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

lo g_{8} (\frac{w ^{4} x ^{2}}{yz}) = lo g_{8} (w^{4} x^{2}) - lo g_{8} (yz)

= lo g_{8} (w^{4} x^{2}) - lo g_{8} (yz)

lo g_{8} (w^{4} x^{2}) = 4 lo g_{8} (w) + 2 lo g_{8} (x)

lo g_{8} (yz) = lo g_{8} (y) + lo g_{8} (z)

= 4 lo g_{8} (w) + 2 lo g_{8} (x) - (lo g_{8} (y) + lo g_{8} (z))

Apply the distributive law:

- (a + b) = - a - b

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

= 4 lo g_{8} (w) + 2 lo g_{8} (x) - lo g_{8} (y) - lo g_{8} (z)

ln (x (x + 8))

ln (\frac{8 x}{y})

lo g_{5} (h - 1) + lo g_{5} (h + 3)

lo g_{2} (x lo g_{5} (x))

What is log_{8}((w^4x^2)/(yz)) ?
The solution to log_{8}((w^4x^2)/(yz)) is 4log_{8}(w)+2log_{8}(x)-log_{8}(y)-log_{8}(z)