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

Express in terms of log 2 and log 3:

log 144

Express the following in a form free from logarithm:

2 log x - log y = 1

Express the following in a form free from logarithm:
2 log x + 3 log y = log a

Evaluate the following without using tables :
log₁₀8 + log₁₀25 + 2 log₁₀3 - log₁₀18

Evaluate the following without using tables :
log 4 + `1/3` log 125 - `1/5`log 32

Express log₁₀2 + 1 in the form of log₁₀x .

Solve for x : ` (log 64)/(log 8)` = log x

State, true or false :
`log x/log y` = log x - log y

State, true or false :
log x x log y = log x + log y

If log₁₀ 8 = 0.90, find the value of:

log₁₀ 4