Question

Find the numerical value of the log expression.

log a = 4 log b = -2 log c = -8

(log) √b ÷ a⁷c⁸

(see screenshot)

Answer 1

`\log(a)=4\hspace{5em}\log(b)=-2\hspace{5em}\log(c)=-8 \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \log\left( \cfrac{√(b)}{a^7c^8} \right)\implies \log(√(b))-\log(a^7c^8)\implies \log(√(b))-[\log(a^7)+\log(c^8)] \\\\\\ \log(√(b))~~ - ~~[7\log(a)+8\log(c)]\implies \log(b^{(1)/(2)})~~ - ~~[7\log(a)+8\log(c)] \\\\\\ \cfrac{1}{2}\log(b)~~ - ~~[7\log(a)+8\log(c)]\implies \cfrac{1}{2}\log(b)-7\log(a)-8\log(c) \\\\\\ \cfrac{1}{2}(-2)-7(4)-8(-8)\implies -1-28+64\implies \text{\LARGE 35}`