Question

Solve the following exponential equation. Express your answer as both an exact expression and a decimal approximation rounded to two decimal places.

7^−2x+9 = 608

Answer 1

@vocaloid

Answer 2

two things - there's an extra 2 at the end that shouldn't be there

I assume you got to this part correctly

-2x = ln(608)/ln(7) - 9

dividing both sides by -2 gives us

x = 9/2 - ln(608)/ (2 * ln(7))

also, it says to round to 2 decimal places, so 2.8529108 needs to be rounded to 2.85

Answer 3

do it what i have on the left is right ?

Answer 4

you need to get rid of that last 2 at the end, then it's right

Answer 5

oh i'm sorry you right

Answer 6

Solve the following exponential equation. Express your answer as a decimal approximation rounded to two decimal places.

e^x−7 = 84x

x = __________

Answer 7

is the x in 84 x also an exponent?

Answer 8

yes

Answer 9

e^(x-7) = 8^(4x)

taking the natural log of both sides will eliminate the e on the left side and give us ln(8^(4x)) on the right side

x - 7 = ln ( 8^(4x) )

using our log rules, you can bring that 4x down from inside the log, to right in front of the log

x - 7 = 4x * ln(8)

can you take it from here? move your x terms to one side, factor out x, solve for x

Answer 10

x - xln (2097152)

Answer 11

hm? how did you get this answer?

Answer 12

by simplifying

Answer 13

would recommend reviewing how to solve 1-variable equations when you get a chance
from here:

x - 7 = 4x * ln(8)

we can move our x-terms to one side by subtracting 4x*ln(8) from both sides
we can also add 7 to both sides to move the 7 to the other side, giving us:

x - 4x(ln8) = 7

factoring out x

x(1-4ln(8)) = 7

dividing both sides by (1-4ln(8))

x = 7/(1-4ln(8))

Answer 14

-0.95657606987

Answer 15

yeah just remember to round to 2 places

Answer 16

-0.95 ?

Answer 17

review rounding when you get a chance

-0.956...

look at the 2nd decimal place. then we look at the next number, 6. because 6 is greater than 5, we round up to -0.96

Answer 18

oh i see

Answer 19

Solve the following exponential equation. Express your answer as a decimal approximation rounded to two decimal places.

e^2x−3 = 13^x/5

Answer 20

x = 2.01747112

Answer 21

good, but remember to round to 2 places

2.017 ---> 7 is greater than 5 so we round up to 2.02

Answer 22

just you can see how it looks