1)log ( ) log ( ) - log ( ) log₂₅125 2)log ( )log₃₄₃ 49 + log₄ log₃ 3) log²₂ log ()...
1)log ( ) log ( ) - log ( ) log₂₅125
2)log ( )log₃₄₃ 49 + log₄ log₃ 3) log²₂ log () 49 * log³ ( ) log₂ 32
1)log ( ) log ( ) - log ( ) log₂₅125 2)log ( )log₃₄₃ 49 + log₄ log₃ 3) log²₂ log ()...
1)log ( ) log ( ) - log ( ) log₂₅125
2)log ( )log₃₄₃ 49 + log₄ log₃ 3) log²₂ log () 49 * log³ ( ) log₂ 32
1)log ( ) log ( ) - log ( ) log₂₅125
2)log ( )log₃₄₃ 49 + log₄ log₃ 3) log²₂ log () 49 * log³ ( ) log₂ 32
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1)
Recall that log(ab) = log(a) + log(b) and log(a/b) = log(a) - log(b).
Using these properties, we can simplify the expression:
log(125) = log(25 * 5) = log(25) + log(5) = 2log(5) + log(5) = 3log(5)
Therefore, the expression becomes:
log() log() - log(3) log(125)
= log() + log() - log(3) * 3log(5)
= log() + log() - 3log(3log(5))
= log() + log() - 9log(5)
2)
Similarly, using the properties of logarithms, we can simplify the expression:
log(343) = log(7^3) = 3log(7)
Therefore, the expression becomes:
log() log(343) 49 + log(4) log(3)
= log() 3log(7) + log() log(49) + log() log(3)
= log() + 3log(7) + 2log(7)
= log() + 5log(7)
3)
Again, using the properties of logarithms, we can simplify the expression:
log(32) = log(2^5) = 5log(2)
Therefore, the expression becomes:
log²(2) log() log() log(32)
= log(2) log() log() 5log(2)
= log(2) log() + log() * 5log(2)
= log(2) + 5log(2)