What is log_{2}((x^6y^7)/8) ?

The solution to log_{2}((x^6y^7)/8) is 6log_{2}(x)+7log_{2}(y)-3

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simplify log_{2}((x^6y^7)/8)

simplify

lo g_{2} (\frac{x ^{6} y ^{7}}{8})

6 lo g_{2} (x) + 7 lo g_{2} (y) - 3

Solution steps

lo g_{2} (\frac{x ^{6} y ^{7}}{8})

Apply log rule:

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

lo g_{2} (\frac{x ^{6} y ^{7}}{8}) = lo g_{2} (x^{6} y^{7}) - lo g_{2} (8)

= lo g_{2} (x^{6} y^{7}) - lo g_{2} (8)

lo g_{2} (x^{6} y^{7}) = 6 lo g_{2} (x) + 7 lo g_{2} (y)

lo g_{2} (8) = 3

= 6 lo g_{2} (x) + 7 lo g_{2} (y) - 3

2 lo g_{5} (a) - 4 lo g_{5} (b)

lo g_{10} (2) - lo g_{10} (14)

lo g_{2} (x^{2} - 3 x + 2) - lo g_{2} (x - 1)

2 lo g_{10} (5) - lo g_{10} (15) + lo g_{10} (9)

lo g_{3} (\frac{3}{y})

What is log_{2}((x^6y^7)/8) ?
The solution to log_{2}((x^6y^7)/8) is 6log_{2}(x)+7log_{2}(y)-3