What is log_{3}((x^8y^4)/6) ?

The solution to log_{3}((x^8y^4)/6) is 8log_{3}(x)+4log_{3}(y)-1-log_{3}(2)

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simplify log_{3}((x^8y^4)/6)

simplify

lo g_{3} (\frac{x ^{8} y ^{4}}{6})

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

Solution steps

lo g_{3} (\frac{x ^{8} y ^{4}}{6})

Apply log rule:

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

lo g_{3} (\frac{x ^{8} y ^{4}}{6}) = lo g_{3} (x^{8} y^{4}) - lo g_{3} (6)

= lo g_{3} (x^{8} y^{4}) - lo g_{3} (6)

lo g_{3} (x^{8} y^{4}) = 8 lo g_{3} (x) + 4 lo g_{3} (y)

lo g_{3} (6) = 1 + lo g_{3} (2)

= 8 lo g_{3} (x) + 4 lo g_{3} (y) - (1 + lo g_{3} (2))

Apply the distributive law:

- (a + b) = - a - b

- (1 + lo g_{3} (2)) = - 1 - lo g_{3} (2)

= 8 lo g_{3} (x) + 4 lo g_{3} (y) - 1 - lo g_{3} (2)

ln (x^{13} 2 - x)

lo g_{10} (x - 2) + lo g_{10} (x) - lo g_{10} (8)

lo g_{10} (z x^{8})

\frac{1}{2} lo g_{2} (405)

- lo g_{10} (6.32 \cdot 1 0^{- 8})

What is log_{3}((x^8y^4)/6) ?
The solution to log_{3}((x^8y^4)/6) is 8log_{3}(x)+4log_{3}(y)-1-log_{3}(2)