SOLUTION: Express as a sum, difference, and product of logarithms, without using exponents. log b 4 square root x^5b^9 / y^7z^10

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Question 302096: Express as a sum, difference, and product of logarithms, without using exponents.
log b 4 square root x^5b^9 / y^7z^10
Answer by london maths tutor(243) About Me  (Show Source):
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log b 4 square root x^5b^9 / y^7z^10
= 1/2* logb 4* (x^5b^9 / y^7z^10)
= 1/2*logb 4 + 1/2*logb (x^5b^9 / y^7z^10)
= 1/2*logb 4 + 1/2*logb (x^5b^9) - 1/2*logb (y^7z^10)
= 1/2*logb 4 + 1/2*logb (x^5) + 1/2*logb (b^9)-1/2*log(y^7) + 1/2*log(z^10)
= 1/2*logb 4 + 5/2*logb (x) + (9/2) - 7/2*log (y) + 5* log(z)