log題目

(1)
X = ³√4²
X = 2 ^ (4/3)
log(base 2) X = 4/3

(2)
log 18
= log (2x3x3)
= log 2 + log 3 + log 3
= a + 2b

log 15
= log (3x10/2)
= log 3 + log 10 - log 2
= b + 1 - a

log 21/4+1/2log4/49-log15
= log [ (21/4)*(2/7) / 15 ]
= log (1/10)
= -1

X=³√4²
...=2^(4/3)
log(低2)x
=log(低2) 2^(4/3)
=4/3

log 18
=log (2x3^3)
=log 2+ log 3^3
=a+3 log^3
=a+3b

log15
=log(300/20)
=log300-log20
=log(3x10x10)-log(2x10)
=log3+log10+log10-log2-log10
=b-a+1

log 21/4+1/2log4/49-log15
=log (21/4)+log (4/49)^(1/2)-log15
=log (21/4)+log (2/7)-log15
=log[ (21/4)(2/7) / 15]
=log(1/10)
= -1

1. x=³√4²
find the log(低2)x

x=³√4²
x=4^(2/3)
x=2^(4/3)
log(base 2)x=4/3

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2.log2=a log 3=b
express the following in terms of a and b

1) log 18
=log(2*9)
=log2+log9
=log2+log3^2
=log2+2log3
=a+2b

2) log15
=log(5*3)
=log5+log3
=log(10/2)+log3
=log10-log2+log3
=1-a+b

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3. without using a calculator, find the value of log 21/4+1/2log4/49-log15

log (21/4)+1/2[log(4/49)]-log15
=log21-log4+1/2[log4-log49)]-log15
=log21-log4+log2-log7-log15
=log(7*3)-2log2+log2-log7-log(5*3)
=log7+log3-2log2+log2-log7-log5-log3
=-log2-log5
=-(log2+log5)
=-1

1) X = ³√4²
= 2 ^ ( 4 / 3 )

Therefore,
log(base2) x = 4/3 log(base2) 2
= 4 / 3

2 I ) log18 = log3x3x2 = log 3 + log 3 + log 2 = 2 log3 + log2 = a + 2b

II ) log15 = log3x5 = log3 + log 5 = b + log10/2 = b + log10 - log2 = a + b - 1


log 21/4 + 1/2 log4/49 - log15
= log21/4 + log2/7 - log3x5
= log21 - log 4 + log2 - log7 - log3 - log5
= log3x7 - 2log2 + log2 - log7 - log3 - log10/2
= log3 + log7 - log2 - log7 - log3 - log10 + log2
= - 1