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

Answer:

Step-by-step explanation:

$Log \ a*b = log \ a + log \ b\\\\\\log \dfrac{a}{b} = log \ a - log \ b\\\\log_{2} \dfrac{x^{6}y^{7}}{8}=log_{2} \ x^{6} + log_{2} \ y^{7} - log_{2} \ \ 8\\\\=6log_{2} \ x + 7log_{2} \ y - log_{2} \ 2^{3}\\\\=6log_{2} \ x + 7log_{2} \ y - 3log_{2} \ 2\\\\\\=6log_{2} \ x + 7log_{2} \ y - 3*1\\\\\\=6log_{2} \ x + 7log_{2} \ y - 3$