Express in Terms of Log 2 and Log 3 : Log 36

Express in terms of log 2 and log 3 : log 36

Sum

log 36 = log( 2 x 2 x 3 x 3 )
= log( 2² x 3² )
= log( 2² ) + log( 3² ) ....[ log_amn = log_am + log_an ]
= 2log2 + 2log3 .....[ log_amⁿ = nlog_am ]

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Laws of Logarithm

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Chapter 8: Logarithms - Exercise 8 (B) [Page 106]

Chapter 8 Logarithms
Exercise 8 (B) | Q 1.1 | Page 106

Express in terms of log 2 and log 3:

log 144

Express in terms of log 2 and log 3:

`log26/51 - log91/119`

Express in terms of log 2 and log 3 :
`"log"75/16 - 2"log"5/9 + "log"32/243`

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

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

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

If log 2 = 0.3010 and log 3 = 0.4771; find the value of : log 3.6

If log₁₀2 = a and log₁₀3 = b ; express each of the following in terms of 'a' and 'b': log `2 1/4`

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

State, true or false : log 1 x log 1000 = 0