What is 7log_{2}(y)-4log_{2}(x) ?

The solution to 7log_{2}(y)-4log_{2}(x) is log_{2}((y^7)/(x^4))

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simplify 7log_{2}(y)-4log_{2}(x)

simplify

7 lo g_{2} (y) - 4 lo g_{2} (x)

lo g_{2} (\frac{y ^{7}}{x ^{4}})

Solution steps

7 lo g_{2} (y) - 4 lo g_{2} (x)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

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

= lo g_{2} (y^{7}) - 4 lo g_{2} (x)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

4 lo g_{2} (x) = lo g_{2} (x^{4})

= lo g_{2} (y^{7}) - lo g_{2} (x^{4})

Apply log rule:

lo g_{c} (a) - lo g_{c} (b) = lo g_{c} (\frac{a}{b})

lo g_{2} (y^{7}) - lo g_{2} (x^{4}) = lo g_{2} (\frac{y ^{7}}{x ^{4}})

= lo g_{2} (\frac{y ^{7}}{x ^{4}})

ln (e^{x} x^{3} (x + 1)^{4})

ln (8) - 2 ln (4)

ln (x y^{2}) - 2 ln (y)

ln (- i e^{π})

ln (x - 2) - ln (x + 2) + 2 ln (x)

What is 7log_{2}(y)-4log_{2}(x) ?
The solution to 7log_{2}(y)-4log_{2}(x) is log_{2}((y^7)/(x^4))