Question

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

Answer 1

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.