Question

if 2^a+3^b=17 and 2^a+b-3^b+1=5,then (a,b)=
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Answer 1

Step-by-step explanation:

Let, 2a=x and

3b=y

Therefore the equation reduces to:

x+y=17;

The second equation can be interpreted in two ways:

2a+2−3b+1=5

2a+2−3b+1=5 which means

2a−3b=2

Now assuming (1) is correct

2a+2=4∗2a=4x and

3b+1=3∗3b=3y

Hence the equations are reduced to:

x+y=17

4x−3y=5

Solving we get x=8 and y= 9

Which implies that,

a=3 and b =2, (convince yourself that this is the only solution as ax for all a>0 is continuous and monotonic.)