If 2^2x= 2^3what is the value of x?

x=2

Step-by-step explanation:

IF the (^) is symbolizing exponents than it works like this:

exponents is just the 'base' or larger number multiplied by itself for example 2^3 would be 2×2×2.

and 2×2×2=8

(2^2x=8)

2^2 would be be equivalent to 2×2 which equals 4.

(4x=8)

that mean we need to figure out what multipled by 4 gets 8.

the reason its multiplied is because when x is written next to a number like that it means it gets multiplied to the other number.

now, if 2×2×2=8 and 2×2=4 that means 4×2=8 which makes x 2

therefore x=2

proof

2^2(2)=2^3

2^2(2)=8

4(2)=8

8=8

(a) common ratio in the given sequence is, 3

(b) push ups will do kendall do on the 20th week

step-by-step explanation:

geometric sequence is a sequence of numbers that follows a pattern were the next term is found by multiplying by a constant called the common ratio(r)

(a)

given the sequence: 6 , 18 , 54 , 162 ,

this sequence is geometric sequence where each term is 3 times the previous term.

therefore,

common ratio(r) = 3.

(b)

a formula for nth term of geometric sequence is given by;

,   where r is the common ratio between the successive terms and is the first term,

to find how many push ups will kendall do on the 20th week.

here. n = 20th term.

in the given sequence first term

then;

simplify:

therefore, push ups will do kendall do on the 20th week