Question

log question..... Let's solve it

Answer 1

log (16/15)^7×(25/24)^5×(81/80)^3
=log (2^28×5^10×3^12)/(3^7×5^7×2^15×3^5×2^12×5^3)
=log 2^1×5^0×3^0
=log 2

Answer 2

Given : 7 log(16/15) + 5 log(25/24) + 3 log(81/80)

We know that a log m = log (m)^a.

= > log (16/15)^7 + log(25/24)^5 + log(81/80)^3

We know that log a + log b + log c = log(abc)

= > log((16/15)^7 + (25/24)^5 + (81/80)^3)

= > log((2^4/3 * 5)^7 + ((5^2)/2^3 * 3)^5 + ((3^4/2^4 * 5)^3)

= > log[(2^28/3^7 * 5^7) + (5^10/2^15 * 3^5) + (3^12/2^12 * 5^3)]

= > log(2^(28 - 15 - 12) + 5^(10 - 7 - 3) + 3^(12 - 7 - 5))

= > log(2^(1) + 5^(0) + 3^(0))

= > log(2).

Therefore, the answer is option (4).

Hope this helps!