Question

Solve 7.74x + 3 = 10.2

Answer 1

x ≈ –2.15

x ≈ –0.47

x ≈ 0.03

x ≈ 0.28

Answer 2

\[7.7^{4x+8}=10.2\]

Answer 3

@Teinis

Answer 4

I got 0.93 but it isn't in the answer choices

Answer 5

Ok I'm gunna try walk you through this one so you get the correct answer yourself.

Answer 6

What did you do first?

Answer 7

I really don't know I am confused :(

Answer 8

Well ok. First off with take the log of both sides again

Answer 9

(x+3)log[7.74] = log[10.2].
Divide both sides by log[7.74], giving
x+3 = log[10.2]/log[7.74].
Subtract 3 from both sides, giving
x = log[10.2]/log[7.74] - 3 ≈ -1.86

Answer 10

\[\ln 7.7^{4x+8} = \ln10.2\]

Answer 11

bUT -1.86 ISN'T AN ANSWER CHOICE

Answer 12

see on the first step, you can't take out x+3 to the front like that

Answer 13

you have to take out the whole thing, so (4x+3)

Answer 14

Ok then is it this:
Subtract 3 from both sides, giving
7.74^x = 7.2.
Take logs, giving
x·log[7.74] = log[7.2].
Divide both sides by log[7.74], giving
x = log[7.2]/log[7.74] ≈ 0.96

Answer 15

But 0.96 isn't an answer choice

Answer 16

wait i'm confussed, is the equation \[7.7^{4x+3} = 10.2\]
or
\[7.7^4x + 3= 10.2\]

Answer 17

Because if it's the first one then you cannot subtract 3 from both sides

Answer 18

The first one

Answer 19

Ok so then let's continue from after we take the logs

Answer 20

move the whole 4x+3 to the front, so you get:
\[(4x+3)\ln 7.7 = \ln10.2\]

Answer 21

Divide both sides by ln 7.7

Answer 22

ok..

Answer 23

\[4x+3 = \frac{ \ln10.2 }{ \ln7.7}\]

Answer 24

Now we can subtract 3 from both sides

Answer 25

then we divide x?

Answer 26

oh we subtract 3 and divide 4

Answer 27

Yes exactly

Answer 28

to get x alone i see

Answer 29

so would the equation look like this

Answer 30

Your first answer of -1.86 was almost correct actually, you just forgot to divide by 4 at the end

Answer 31

ty

Answer 32

No problem