Question

Let 3^a=4,4^b=5,5^c=6,6^d=7,7^e=8 and 8^f=9. The value of product (abcdef) is

Answer 1

Given that 3^a=4, 4^b=5, 5^c=6, 6^d=7, 7^e=8, 8^f=9
since 3^a=4 ------(1)
and 4^b=5. ------(2)
from equation (1) we can write 4 as 3^a
(3^a)^b = 5
3^(ab) = 5
similarly,
(3^ab)^c = 6
3^(abc) = 6

(3^abc)^d = 7
3^(abcd) = 7

(3^abcd)^e = 8
3^(abcde) = 8

(3^abcde)^f = 9
3^(abcdef) = 3^2
since bases are same so we can compare the exponents
abcdef = 2