Задание 4.26

4.26. Найдите x, если:
1) log ax = 3log a2 + 2log a3; 3) lg x = 2 5 lg 32 1 3 lg 64 + 1.
2) log ax = 1 4 log a16 + 3log a0,5

Answers

1) log ax = 3log a2 + 2log a3
log ax = 2log a2 + 2log a3 + log a2
log ax = 2log a6 + log a2
log ax = log ab + log a2 + log a6
log ax = log a12 + log a6
log ax = log a72
x = 72
2) log ax = 1 4 log a16 + 3log a0,5
log ax = 1 4 log a (1 2 ) 4 + 3log a (1 2 )
log ax = 1 4 (4) log a (1 2 ) + 3log a (1 2 )
log ax = log a (1 2 ) + 3log a (1 2 )
log ax = 2log a (1 2 )
log ax = log a (1 2 ) 2
x = 1 4
3) lg x = 2 5 lg 32 1 3 lg 64 + 1
lg x = 2 5 lg (2)5 1 3 lg (43) + 1
lg x = 2 5 5lg 2 1 3 3lg 4 + 1
lg x = 2lg 2 lg 4 + 1
lg x = lg 4 lg 4 + 1
lg x = 1
x = 10

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2022-01-08 10:20
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