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Logarithm Issues



Drawback 1 :

Discover the logarithm of 64 to the bottom 2√2.

Resolution :

Write 64 as by way of 2√2.

64 = 26

= 24+2

= 2 22

= 2⋅ [(√2)2]2

= 2⋅ (√2)4

= (2√2)4

log2√264 = log2√2(2√2)4

= 4log2√2(2√2)

= 4(1)

= 4

Drawback 2 :

If logabc = x, logbca = y and logcab = z, then discover the worth of

1/(x + 1) + 1/(y + 1) + 1/(z + 1)

Resolution :

x + 1 = logabc + logaa = logaabc

y + 1 = logbca + logbc = logbabc

z + 1 = logcab + logcc = logcabc

1/(x + 1) = 1/logaabc = logabca

1/(y + 1) = 1/logbabc = logabcb

1/(z + 1) = 1/logcabc = logabcc

1/(x + 1) + 1/(y + 1) + 1/(z + 1) = logabca + logabcb + logabcc

= logabcabc

= 1

Drawback 3 :

If a = log2412, b = log3624 and c = log4836, then discover the worth of (1 + abc) by way of b and c.

Resolution :

1 + abc = 1 + log2412  log3624 ⋅ log4836

= 1 + log3612 ⋅ log4836

= 1 + log4812

= log4848 + log4812

= log48(48 ⋅ 12)

= log48(2 ⋅ 12)2

= 2log4824

= 2log3624 ⋅ log4836

= 2bc

Drawback 4 :

Discover the worth of log 0.0001 to the bottom 0.1.

Resolution :

log0.10.0001 = log0.1(0.1)4

= 4log0.10.1

= 4(1)

= 4

Drawback 5 :

If 2logx = 4log3, then discover the worth of x.

Resolution :

2logx = 4log3

Divide either side by 2.

logx = 2log3

logx = log32

logx = log9

x = 9

Drawback 6 :

Discover the worth of log√264.

Resolution :

log√264 = log√2(2)6

= 6log√2(2)

= 6log√2(√2)2

= 6 ⋅ 2log√2(√2)

= 12 ⋅ 2(1)

= 12

Drawback 7 :

Discover the worth of log (1/81) to the bottom 9.

Resolution :

log9(1/81) = log91 – log981

= 0 – log9(9)2

= -2log99

= -2(1)

= -2

Drawback 8 :

Discover the worth of log(0.0625) to the bottom 2.

Resolution :

log2(0.0625) = log2(0.5)4

= 4log2(0.5)

= 4log2(1/2)

= 4(log21 – log22)

= 4(0 – 1)

= 4(-1)

= -4

Drawback 9 :

Given log2 = 0.3010 and log3 = 0.4771, discover the worth of log6.

Resolution :

log6 = log(2 ⋅ 3)

= log2 + log3

Substitute the values of log2 and log3.

= 0.3010 + 0.4771

= 0.7781

Drawback 10 :

Discover the worth of log(0.3) to the bottom 9.

Resolution :

log9(0.3) = log9(1/3)

= log91 – log93

= 0 – log93

= -log93

= -1 / log39

= -1 / log332

= -1 / 2log33

= -1 / 2(1)

= -1/2

Video Classes

Introduction to Logarithms

Elementary Legal guidelines of Logarithms

Change of Base

Utilizing Log Desk

Utilizing Antilog Desk

Vital Stuff

Distinction between Bar Worth and Adverse Worth

Multiplication of Two Logarithms

Relationship between Exponents and Logarithms

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