1.

Let 3^a=4, 4^b=5, 5^c=6, 6^d=7, 7^e=8, 8^f=9 then find the value od the product abcdef.

Answer»

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
Hope it helps!!!!!


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