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 \

Question

Inessa05 [86]

3 years ago

13

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

Mathematics

1 answer:

bija089 [108] · Answer 1 · 2022-06-14T05:59:55+03:00

bija089 [108]3 years ago

6 0

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)