For any integer k greater than 1, the symbol k* denotes the product of all the fractions of the form 1/t, where t is an integer between 1 and k, inclusive. What is the value of 5*/4*?

1/5

Step-by-step explanation:

If k* denotes the product of all the fractions of the form 1/t, where t is an integer between 1 and k inclusive. Inclusive means 1 and k values will be included as the integers.

To get value of 5*;

Since 5 is greater than 1, the fraction in form if 1/t where t is the integer between 1 and 5 inclusive are;

1/1, 1/2, 1/3, 1/4 and 1/5 since 1,2,3,4 and 5 are the values between 1 and 5 "inclusive"

5* will be the product of this fractions i.e 1×1/2×1/3×1/4×1/5 = 1/120

Similarly for 4*;

the fraction in form if 1/t where t is the integer between 1 and 4 inclusive are;

1/1, 1/2,1/3 and 1/4 since 1,2,3 and 4 are the values between 1 and 4 "inclusive"

4* value will be the product of this fractions i.e 1× 1/2×1/3 ×1/4 = 1/24

5*/4* = (1/120)/(1/24)

5*/4* = 1/120×24/1

5*/4* = 1/5

x =-.20752

step-by-step explanation:

4^(x+2)=12

4^(x+2)=12

take the log base 4 on each side

log 4 (4^(x+2) = log 4(12)

we know log b(a^y) = y log b (a)

(x+2) log 4(4) = log 4 (12)

x+2 = log 4 (12)

we know   logb c = loga c/loga b

we want to convert to base 10   so a = 10

by default, we do not write the 10   c = 4   and b = 10

log4 10 = log 12/log 4

log4 10 = log 12/ log 4

x+2 = log 12/ log 4

subtract 2 from each side

x +2 -2 = log 12/ log 4 -2

x = 1.79248125 -2

x =-.20752

m

step-by-step explanation: