Express in Terms of Log 2 and Log 3 : Log 36

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

योग

log 36 = log( 2 x 2 x 3 x 3 )
= log( 2² x 3² )
= log( 2² ) + log( 3² ) ....[ log_amn = log_am + log_an ]
= 2log2 + 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 1.1 | पृष्ठ १०६

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 :
log 5 + log 8 - 2 log 2

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 `

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

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 25

If log₁₀2 = a and log₁₀3 = b ; express each of the following in terms of 'a' and 'b' : log 5.4

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

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.