Question

plzzz solve it fast no. 29

Answer 1

a = log( 12 base 24)
b = log( 24 base 36 )
c = log( 36 base 48 )

we know , by property of logarithm
log ( a base b ) = log( a base e )/log ( b base e )

use this here,

a = log( 12 base 48 ) = log(12 base e)/log(48 base e) =ln12/ln24

b = log( 24 base 36) = log( 24 base e)/log( 96 base e) =ln24/ln36

c = log( 36 base 48) = log(32 base e )/log( 48 base e) =ln36/ln48


now ,

LHS = 1+ abc

= 1+ { ln12/ln24}{ln24/ln36}{ln36/ln48}

= 1 + { ln12/ln48 }

={ln48 + ln12}/ln48

=ln12 × 48/ln48

=ln(12×12×2×2)/ln48

=ln(24²)/ln48

=2ln24/ln48

multiply numerator and denominator with ln36

=2 ln24×ln36/ln36×ln48

=2×{ln24/ln36}{ln36/ln48}

=2×b ×c =2bc =RHS