Which expression is equivalent to 2 5 (2 ^ 11)/(5 ^ 29) (2 ^ 10)/(5 ^ 13) (2 ^ 11)/(5 ^ 14) (2 ^ 11)/(5 ^ 31) 2*5^ -1 *( 2 5^ 3
1 answer:
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Answer:
a) 3
b) 9
c) 81
d) x
Step-by-step explanation:
We know the properties of log function as:
1) log(AB) = log(A) + log(B)
2)
3) log(aᵇ) = b × log(a)
also,
4)
Given:
a. y =
Now,
taking log both sides, we get
log(y) =
using 3, we get
log(y) = log₃(3) × log(3)
using 4, we get
log(y) = × log(3)
or
log(y) = 1 × log(3)
taking anti-log both sides
y = 3
b. y =
Now,
taking log both sides, we get
log(y) =
using 3, we get
log(y) = log₃(9) × log(3)
using 4, we get
log(y) = × log(3)
or
log(y) = log(9)
taking anti-log both sides
y = 9
c. y =
Now,
taking log both sides, we get
log(y) =
using 3, we get
log(y) = log₃(81) × log(3)
using 4, we get
log(y) = × log(3)
or
log(y) = log(81)
taking anti-log both sides
y = 81
d. y =
Now,
taking log both sides, we get
log(y) =
using 3, we get
log(y) = log₃(x) × log(3)
using 4, we get
log(y) = × log(3)
or
log(y) = log(x)
taking anti-log both sides
y = x