Express Log102 + 1 in the Form of Log10x. - Mathematics

Express log₁₀2 + 1 in the form of log₁₀x .

योग

log₁₀2 + 1

= log₁₀2 + log₁₀10 ....[ ∵ log₁₀10 = 1 ]

= log₁₀2 x 10 ....[ log_am + log_an = log_amn ]

= log₁₀20.

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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 6 | पृष्ठ १०६

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 4 + `1/3` log 125 - `1/5`log 32

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

Solve for x : log (x² - 21) = 2.

If log₁₀2 = a and log₁₀3 = b ; express each of the following in terms of 'a' and 'b': log 12

If log₁₀2 = a and log₁₀3 = b ; express each of the following in terms of 'a' and 'b': log `2 1/4`

If log₁₀2 = a and log₁₀3 = b; express each of the following in terms of 'a' and 'b' : log `3 1/8`

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.