Question

log4 7-log8 7+2log32 7
помогите, пожалуйста!

Answer 1

формула

$log_{a^k}b= frac{1}{k}log_{a}b$

$log_{4}7=log_{2^2}7= frac{1}{2}log_{2}7 \ \ log_{8}7=log_{2^3}7= frac{1}{3}log_{2}7 \ \ log_{32}7=log_{2^5}7= frac{1}{5}log_{2}7$

Формула
$ncdot log_{a}b=log_{a}b^n$

$log_{4}7=log_{2^2}7= frac{1}{2}log_{2}7=log_{2}7^{ frac{1}{2} }=log_ {2} sqrt{7} \ \ log_{8}7=log_{2^3}7= frac{1}{3}log_{2}7 =log_{2} sqrt[3]{7} \ \ 2log_{32}7=2log_{2^5}7= 2cdot frac{1}{5}log_{2}7=log_{2}7^{ frac{2}{5} }$

Формулы
$log_{a}b-log_{a}c=log_{a} frac{b}{c} \ \ log_{a} frac{b}{c}+log_{a}d=log_{a} frac{b}{c}cdot d$

log₄ 7-log₈ 7+2log₃₂ 7=(1/2)log₂7-(1/3)log₂7+2·(1/5)log₂7=
=log₂√7-log₂∛7+log₂7²/⁵=log₂(√7/∛7)·7²/⁵=log₂7¹⁷/³⁰