Question

If 1 ^ x, 5 ^ x and 7 ^ x are in A.P. and also in G.P. then the value of 'x' is

Answer 1

Answer:

Step-by-step explanation:

IN AN A.P,

2b=a+c

2.5∧x =1^x+7^x

2.5^x=1+7^x    -------1

IN G.P,

b²=ac

(5^x)²=(7^x) (1^x)

LET US ASSUME 5^x=a

7^x=a²

take first equation,

2.a=1+a²

a²-2a+1=0

(a-1)²=0

⇒a=1

5^x=1  or 7^x=1

⇒x=㏒1 to the base 5

(or)

⇒x=log1 to the base 7