Question

Which of the following is the solution to the equation 8^y + 2) = 2^ y?

Answer 1

a) y = 1
b) y= 3
c) y= -3
d) y= -1

Answer 2

What you can do is plugin each of the possible answers... But I will show you how to solve.

Answer 3

First, you need to distribute the 8:
8(y + 2) = 8y + 16
Ok then lets try your answer and see what we get.

Answer 4

ok then we are stuck with the same problem. Why dont we try inserting the variable and then add before we distribute.

Answer 5

8(y + 2) What do you want to try first?

Answer 6

distribute?

Answer 7

you start with
8(y + 2) = 2y

britanny has the right idea: distribute the 8

8y + 16 = 2y
now add -2y to both sides
8y -2y + 16 = 2y + -2y
simplify
6y + 16 = 0
add -16 to both sides
6y = 16

divide both sides by 6
y = 16/6 = 8/3

are you sure you typed in the correct question ?

Answer 8

now look i added ^ those thangs sorry.

Answer 9

yes, that makes more sense
\[ 8^{y+2} = 2^y \]

the trick is to know that 8= 2*2*2 , or 2^3
\[ \left(2^3\right)^{y+2} = 2^y \]
use the rule that
\[ \left(x^a\right)^b= x^{ab} \]
to rewrite the problem as
\[ 2^{3(y+2)} = 2^y \]

now set the exponents equal to each other
3(y+2) = y

can you solve this ?

Answer 10

no

Answer 11

3(y+2) = y

distribute the 3 on the left side.

Answer 12

3y+6=y ?

Answer 13

yes, now add -y to both sides:
3y+ -y + 6=y + -y
can you simplify that ?

Answer 14

3+6=y ? idk that one confused me

Answer 15

3y+ -y + 6=y + -y

on the right side you have y + -y which says " 1y take away 1 y" (you get zero)
on the left side you have 3 y and take away 1 y
can you do it now ?

Answer 16

3y+6=y ?

Answer 17

that is what you start with. now add -y to both sides

3y -y + 6 = y -y

what is y-y ?

Answer 18

y-y is nothing? just 0

Answer 19

yes, so
3y -y + 6 = y -y
simplifies (on the right side) to
3y - y + 6 = 0

now what is 3 y's take away 1 y ?

Answer 20

2y's

Answer 21

so now you have
2y + 6 =0

next, add -6 to both sides. can you do that ?

Answer 22

2y + 6 -6 = 0-6 or
2y = -6

now divide both sides by 2

Answer 23

-3 is the answer??

Answer 24

yes

Answer 25

thanks