Question

Solve this.
Give appropriate calculations.Lazy answers will be deleted

Answer 1

a = log{ 12 base 24 }
b = log{ 24 base 36 }
c = log{ 36 base 48 }

we know ,
log{ a base b } = log{ a base e }/log{ b base e }
use this concept here,

now,
abc = log{ 12 base 24} × log{ 24 base 36 } × log{ 36 base 48 }

= log12/log24 × log24/log36 × log36/log48

= log12/log48

now,

LHS 1 + abc = 1 + log12/log48

=log48/log48 + log12/log48

=( log48 + log12)/log48

=log(48 × 12)/log48

=log( 24 × 24 )/log48

= 2log24/log48

= 2{ log24/log36 }{ log36/log48}

= 2log{ 24 base 36 }.log{ 36 base 48 }

=2bc