выразите log 30 по основанию 8 через a и b, если lg5=a, lg3=b. Created by brabrainly. algebra-ru

выразите log 30 по основанию 8 через a и b, если lg5=a, lg3=b...

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June 2022 1 17 Report

выразите log 30 по основанию 8 через a и b, если lg5=a, lg3=b

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NNNLLL54

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$lg5=a\; ,\; \; lg3=b\\\\log_830=\frac{lg30}{lg8}=\frac{lg(5\cdot 3\cdot 2}{lg2^3}=\frac{lg5+lg3+lg2}{3lg2}=\\\\=\frac{a+b+lg2}{3\cdot lg2}=\frac{a+b+(1-a)}{3\cdot (1-a)}=\frac{b+1}{3\cdot (1-a)}$

$\star \; \; lg2=lg\frac{10}{5}=lg10-lg5=1-a\; \; \star$

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