State, True Or False : Log25/Log 5 = Log X, Then X = 2 - Mathematics

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

Sum

Given that
`log 25/log 5` = log x

⇒ `[ log 5 xx 5 ]/[ log 5 ]` = log x

⇒ `[ log5^2 ]/[ log 5 ] = log x`

⇒ `[ 2log5 ]/[ log5 ] = log x ...[ log_am^n = nlog_a m ]`

⇒ 2 = log₁₀x
⇒ 10² = x
⇒ x = 100
Thus, the statement, x = 2 is false.

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Laws of Logarithm

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Chapter 8: Logarithms - Exercise 8 (B) [Page 107]

Chapter 8 Logarithms
Exercise 8 (B) | Q 10.3 | Page 107

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:
2 log x + 3 log y = log a

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

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

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

Express log₁₀2 + 1 in the form of log₁₀x .

Solve for x : log₁₀ (x - 10) = 1

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

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.

If log₁₀ 8 = 0.90; find the value of : log₁₀ 4