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

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:

2 log x - log y = 1

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

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

Find x, if : x - log 48 + 3 log 2 = `1/3`log 125 - log 3.

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

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

State, true or false :
`log x/log y` = log x - log y

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.