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 36

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 :
log 5 + log 8 - 2 log 2

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

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:

`2/3` log 8

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

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