Which choice shows the best estimate of the product 0.51 × 783?

a.1/2 × 800

b.1 × 1,000

c.5 × 700

d.50 × 800

Step-by-step explanation:

We are given to ask a product of 0.51x783

If we want to find out the product without actual multiplication we can round off both factors to nearest and do

0.51 is very near to

783 rounded off would be 800 since

So the product would be approximately

i.e. option A

Option B is incorrect because 1000 is very far from 783

C is wrong because 700 is not correct round off of 783

D is wrong since 50 is not round off value of 0.51

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