Express in terms of log 2 and log 3: log 144

Express in terms of log 2 and log 3:

log 144

योग

log 144

= log( 2 × 2 × 2 × 2 × 3 × 3 )
= log( 2⁴ x 3² )
= log( 2⁴ ) + log( 3² ) ....[ log_amn = log_am + log_an]
= 4log2 + 2log3 ....[ log_amⁿ = nlog_am ]

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Laws of Logarithm

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अध्याय 8: Logarithms - Exercise 8 (B) [पृष्ठ १०६]

अध्याय 8 Logarithms
Exercise 8 (B) | Q 1.2 | पृष्ठ १०६

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

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

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 `

Solve for x : log₁₀ (x - 10) = 1

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

`2/3` log 8

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

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

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