What is 7log_{2}(a)+log_{2}(6)-log_{2}(b) ?

The solution to 7log_{2}(a)+log_{2}(6)-log_{2}(b) is log_{2}((3a^7)/b)+1

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simplify 7log_{2}(a)+log_{2}(6)-log_{2}(b)

simplify

7 lo g_{2} (a) + lo g_{2} (6) - lo g_{2} (b)

lo g_{2} (\frac{3 a ^{7}}{b}) + 1

Solution steps

7 lo g_{2} (a) + lo g_{2} (6) - lo g_{2} (b)

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

= 7 lo g_{2} (a) + 1 + lo g_{2} (3) - lo g_{2} (b)

Apply log rule:

b \cdot lo g_{a} (x) = lo g_{a} (x^{b})

7 lo g_{2} (a) = lo g_{2} (a^{7})

= lo g_{2} (a^{7}) + 1 + lo g_{2} (3) - lo g_{2} (b)

Simplify

lo g_{2} (a^{7}) + lo g_{2} (3) - lo g_{2} (b) : lo g_{2} (\frac{3 a ^{7}}{b})

= lo g_{2} (\frac{3 a ^{7}}{b}) + 1

ln (2) + \frac{1}{2} ln (x + 1) - 2 ln (1 + x)

ln (z) - ln (4 y)

lo g_{2} (\frac{x}{4})

\frac{1}{3} lo g_{b} (x) + 4 lo g_{b} (y) - 5 lo g_{b} (x)

lo g_{3} (x) - lo g_{3} (x^{5})

What is 7log_{2}(a)+log_{2}(6)-log_{2}(b) ?
The solution to 7log_{2}(a)+log_{2}(6)-log_{2}(b) is log_{2}((3a^7)/b)+1