Question

5-3^x=-40 round to the nearest ten thousandth
i have no clue what i am doing here.

Answer 1

is this
\[ 5 -3^x = -40 \]?

Answer 2

yes

Answer 3

the first step is add -5 to both sides of the equation and then simplify:
\[-5+ 5 -3^x = -5 -40 \]

Answer 4

okay so you now have 3^x = -45
right

Answer 5

almost. it is -3^x= -45

-3^x is the same as -1* 3^x

so you now have

\[ -1\cdot 3^x = -45 \]
multiply both sides by -1

Answer 6

-3^x=45

Answer 7

multiply both sides by -1
\[ -1\cdot -1\cdot3^x = -1\cdot-45 \]
what do you get ?

Answer 8

3^x=45

Answer 9

much better.

now it is the same problem as the previous one.

Answer 10

log 3 /log 45

Answer 11

you are missing an important idea

if you have
2*x= 4

you can get the x by itself if you divide 2x by 2 (because 2/2 is 1) and 1*x is x
but if you divide the left side by 2, you must divide the right side by 2 to keep things equal.

now in your problem you have
log(3)*x = log(45)

you want the x by itself. what do you divide by to get x by itself ?

Answer 12

3

Answer 13

if you have
log(3) times x
you divide by log(3). not just 3

can you finish
log(3)*x = log(45)

Answer 14

.2886

Answer 15

if you have
log(3) times x
you divide by log(3).

you have
log(3)*x = log(45)

what do you divide both sides by ?

Answer 16

log3

Answer 17

yes. if you divide both sides by log3 you get
log(3)*x/log(3) = log(45)/log(3)

can you simplify this ?

Answer 18

x=log (45)/log(3)

Answer 19

yes, and x is ?

Answer 20

x=3.4650

Answer 21

or is it x=.2886

Answer 22

we can check your answer by putting this into google
5-3^(3.4650)=

if should come out very close to -40

Answer 23

the answer is not x=0.2886. It would be if we started with
log(45) x = log(3)
then to get "x by itself" we would divide both sides by log(45)
but that is not the problem.

Answer 24

-40.0013

Answer 25

right, so in the original problem
5-3^x=-40

the left side is very close to -40 (not exact because we rounded x to the nearest ten thousandth)

so you know x = 3.4650 is the correct answer.