If 10 10 x 2 x 10 find the value of x Given log 2 0 3010 ........

Quantitative Aptitude (CDS) Logarithm

If 10 ^(10-x) = 2 ^ ( x- 10 ) , find the value of x ? ( Given log 2 = 0.3010 )

Explanation:

Given 10^ (10 – x ) = 2^ (x – 10 )
Or 10^ (10 – x ) = 2^ -(10 – x )
Or ( 10- x ) log 10 = - ( 10 – x ) log 2
Or (10 – x) log 10 + ( 10 – x ) log 2 = 0
Or ( 10 – x ) { log 10 + log 2 } = 0
Or ( 10 – x ) ( 1+ 0.3010)= 0
Or 1.3010(10 – x ) = 0
Or 10 – x = 0
Or x = 10