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

Express in terms of log 2 and log 3:

log 144

Sum

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

Chapter 8 Logarithms
Exercise 8 (B) | Q 1.2 | Page 106

Express in terms of log 2 and log 3 : log 4.5

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:
2 log x + 3 log y = log a

Solve for x : log (x - 2) + log (x + 2) = log 5

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

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 5.4

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

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