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

Express in terms of log 2 and log 3:

log 144

बेरीज

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

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

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

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

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

Solve for x : log (x + 5) + log (x - 5) = 4 log 2 + 2 log 3

Solve for x : `(log 81)/(log27 )` = x

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 : log 25

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

Given that log x = m + n and log y = m - n, express the value of log ` ( 10x ) / ( y ^ 2 )` in terms of m and n.