Question

3^(a)=27^(b+1) and 5^(b)=25^(a-1) then a+b=
plz give full solution ​

Answer 1

Answer:

Given that

3^a=27^b+1

=)3^a=3^3(b+1)

=)a=3(b+1)....................(i)

5^b=25^(a-1)

=)5^b=5^2(a-1)

=)b=2(a-1).............(ii)

From equation (i) and (ii)

b=2(a-1)

=)b=2{3(b+1)-1}

=)b=2(3b+3-1)

=)b=6b+4

=)6b+4-b=0

=)5b+4=0

=)5b= -4

=)b= -4/5

putting b values in equation (i)

a=3(b+1)

=)a=3(-4/5+1)

=)a=3(-4+5/5) (taking LCM 5)

=)a=3×1/5

=)a=3/5

therefore

a+b=3/5+(-4/5)

=3/5-4/5

=3-4/5 (LCM 5)

= -1/5

answer....... -1/5