Question

Find the numerical value of the log expression. \log a=7\hspace{15px} \log b=10\hspace{15px} \log c=3 loga=7logb=10logc=3 \log \frac{a^8c^2}{b^3} log b 3 a 8 c 2 ​

Answer 1

Answer:

  32

Step-by-step explanation:

  $\log a=7\hspace{15px} \log b=10\hspace{15px} \log c=3\\\\ \log \dfrac{a^8c^2}{b^3}=8\log{a}+2\log{c}-3\log{b}=(8)(7)+(2)(3)-(3)(10)\\\\=56+6-30=\boxed{32}$

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The applicable rules of logarithms are ...

  log(ab/c) = log(a) +log(b) -log(c)

  log(a^b) = b·log(a)