Logarithms
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Simplify:[1/logxy(xyz)+1/logyz(xyz)+1/logzx(xyz)]
Given expression: logxyz xy+ logxyz yz+ logxyz zx = logxyz (xy*yz*zx)=logxyz (xyz)2 2logxyz(xyz)=2*1=2
Given expression: logxyz xy+ logxyz yz+ logxyz zx
= logxyz (xy*yz*zx)=logxyz (xyz)2
2logxyz(xyz)=2*1=2
See lessIf log10 2=0.30103,find the value of log10 50.
log10 50=log10 (100/2)=log10 100-log10 2=2-0.30103=1.69897.
log10 50=log10 (100/2)=log10 100-log10 2=2-0.30103=1.69897.
See lessEvaluate: log3 27
Let log3 27=33 or n=3. ie, log3 27 = 3.
Let log3 27=33 or n=3.
ie, log3 27 = 3.
See lessIf log 2=.30103,find the number of digits in 256 .
log 256 =56log2=(56*0.30103)=16.85768. Its characteristics is 16. Hence,the number of digits in 256 is 17.
log 256 =56log2=(56*0.30103)=16.85768.
Its characteristics is 16.
Hence,the number of digits in 256 is 17.
See lessFind the value of x which satisfies the relation
Log10 3+log10 (4x+1)=log10 (x+1)+1
log10 3+log10 (4x+1)=log10 (x+1)+1 Log10 3+log10 (4x+1)=log10 (x+1)+log10 (x+1)+log10 10 Log10 (3(4x+1))=log10 (10(x+1)) =3(4x+1)=10(x+1)=12x+3 =10x+10 =2x=7x=7/2
log10 3+log10 (4x+1)=log10 (x+1)+1
Log10 3+log10 (4x+1)=log10 (x+1)+log10 (x+1)+log10 10
Log10 (3(4x+1))=log10 (10(x+1))
=3(4x+1)=10(x+1)=12x+3
=10x+10
=2x=7
x=7/2
See less3log8x=log4(x+6)
3 log8x = log4 (x+6)⇒ 3 log23x = log22 (x+6) (∵ logamb = 1/m logab)⇒ 3/3 log2x = 1/2 log2 (x+6)⇒ 2 log2x = log2 (x+6)⇒ log2x2 = log2 (x+6) (∵ n log a = log an)⇒ x2 = x+6 (By taking anti log)⇒ x2 - x - 6 = 0⇒ x2 - 3x + 2x - 6 = 0⇒ x(x-3) + 2(x-3) = 0⇒ (x+2) (x-3) = 0⇒ x+2 = 0 or x-3 = 0⇒ x = -2(NotRead more
3 log8x = log4 (x+6)
⇒ 3 log23x = log22 (x+6) (∵ logamb = 1/m logab)
⇒ 3/3 log2x = 1/2 log2 (x+6)
⇒ 2 log2x = log2 (x+6)
⇒ log2x2 = log2 (x+6) (∵ n log a = log an)
⇒ x2 = x+6 (By taking anti log)
⇒ x2 – x – 6 = 0
⇒ x2 – 3x + 2x – 6 = 0
⇒ x(x-3) + 2(x-3) = 0
⇒ (x+2) (x-3) = 0
⇒ x+2 = 0 or x-3 = 0
⇒ x = -2(Not possible) or x = 3)
(∵ Domain of log x is x > 0)
Hence, solution is x = 3
See lessEvaluate log34 34
We know that loga a=1,so log34 34=0.
We know that loga a=1,so log34 34=0.
See less