If Log102 = a and Log103 = B; Express Each of the Following in Terms of 'A' and 'B' : Log 60 - Mathematics

If log₁₀2 = a and log₁₀3 = b; express each of the following in terms of 'a' and 'b' : log 60

Sum

log 60
= log₁₀10 x 2 x 3 ...[ log_amn = log_am + log_an ]
= 1 + log₁₀2 + log₁₀3 ...[ ∵ log1010 = 1 ]
= 1 + a + b ...[ ∵ log₁₀2 = a and log₁₀3 = b ]

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Laws of Logarithm

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Chapter 8: Logarithms - Exercise 8 (B) [Page 107]

Chapter 8 Logarithms
Exercise 8 (B) | Q 11.5 | Page 107

Evaluate the following without using tables :
log 5 + log 8 - 2 log 2

Prove that : `2"log" 15/18 - "log"25/162 + "log"4/9 = log 2 `

Find x, if : x - log 48 + 3 log 2 = `1/3`log 125 - log 3.

If log 2 = 0.3010 and log 3 = 0.4771; find the value of : log 25

If log₁₀2 = a and log₁₀3 = b ; express each of the following in terms of 'a' and 'b': log 12

Solve for x :
`log 225/log15` = log x

If log₁₀2 = a and log₁₀3 = b ; express each of the following in terms of 'a' and 'b' : log 5.4

State, true or false :
If `log 25/log 5 = log x`, then x = 2.

Given that log x = m + n and log y = m - n, express the value of log ` ( 10x ) / ( y ^ 2 )` in terms of m and n.

If log₁₀ 8 = 0.90, find the value of:

log₁₀ 4