Question

Assuming all variables are positive, use properties of logarithms to write the expression as a sum or difference of logarithms or multiples of logarithms.

log2 (x⁶y⁷/8)

Answer 1

Explanation:

`Log \ a*b = log \ a + log \ b\\\\\\log (a)/(b) = log \ a - log \ b\\\\log_(2) (x^(6)y^(7))/(8)=log_(2) \ x^(6) + log_(2) \ y^(7) - log_(2) \ \ 8\\\\=6log_(2) \ x + 7log_(2) \ y - log_(2) \ 2^(3)\\\\=6log_(2) \ x + 7log_(2) \ y - 3log_(2) \ 2\\\\\\=6log_(2) \ x + 7log_(2) \ y - 3*1\\\\\\=6log_(2) \ x + 7log_(2) \ y - 3\\\\`