Question

3^a=27^b+1 and 5^b=25^a-1 , then a+b = ​

Answer 1

value of a + b = 1/5

It is given that, 3^a = 27^(b + 1) and 5^b = 25^(a - 1)

and we have to find a + b

3^a = 27^(b + 1)

⇒3^a = (3³)^(b + 1)

⇒3^a = 3^(3 × (b + 1))

⇒3^a = 3^(3b + 3)

⇒a = 3b + 3 .........(1)

again, 5^b = 25^(a - 1)

⇒5^b = 5^{2(a - 1)}

⇒5^b = 5^(2a - 2)

⇒b = 2a - 2 ..........(2)

from equations (1) and (2) we get,

a = 3(2a - 2) + 3

⇒a = 6a - 6 + 3

⇒-5a = -3

⇒a = 3/5

and b = 2 × 3/5 - 2 = -4/5

hence, a + b = 3/5 - 4/5 = 1/5

also read : 1.the value of 5 1/6 [5 is a mixed fraction] divided by 9/2 is equal to

a.31/6

b.1/27

c.5 1/27

d.31/27

2.what is the s...

https://brainly.in/question/1256149

Simplify the following :-

a)5/6*32/25*3/2

b)24/27*6/5*14/8

c)11/25*15/22*4/9

d)18/10*7/8*12/49

e)1/2*4/5*3/7*6/5

f)2/3*9...

https://brainly.in/question/4148085

Answer 2

The value of a + b is -1/5

• Given,

                   $3^{a}=27^{b+1}$

                   $3^{a}=3^{3(b+1)}$

                   $3^{a}=3^{3b+3}$

• Bases are same, equate the powers.

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

• Also,

                     $5^{b}=25^{a-1}$

                     $5^{b}=5^{2(a-1)}$

                     $5^{b}=5^{2a-2}$

• Bases are same, equate the powers.

                      b = 2a - 2

                      b = 2(3b + 3) -2      [from (1)]

                      b = 6b + 6 -2

                      b - 6b = 4

                       -5b = 4

                         b = -4/5

• Substituting 'b' in (1)

                         a = 3(-4/5) + 3

                         5a = -12 + 15

                         5a = 3

                           a = 3/5

• Now,

                          a + b = 3/5 - 4/5

                          a + b = -1/5