Question

Solve 7.74^x + 3 = 10.2

Answer 1

Solving for x? And I bet that you're studying natural logs, right?

Answer 2

common logs, is more like it!

Answer 3

take the log of each side, like this:

Answer 4

\[\log 7.74^{x}=\log(10.2-3)\]

Answer 5

\[\log 7.74^{x}=\log(7.2)\]Log laws tell us that we can move that x exponent to the front to obtain this:

Answer 6

\[x \log (7.74)=\log (7.2)\]in order to solve for x, we will divide log(7.2) by log(7,74) like this:

Answer 7

ok

Answer 8

\[x=\frac{ \log (7.2) }{ \log (7.74) }\]\[x=\frac{ .857332 }{ .888741 }\]

Answer 9

What do you get when you divide that out?

Answer 10

you will find the values for those logs on your calculator.

Answer 11

.9646595964

Answer 12

Yep! Although you probably don't need it to all those decimal places! Talk about accuracy!

Answer 13

x ≈ -2.15
x ≈ -0.47
x ≈ 0.03
x ≈ 0.28

Answer 14

eek, let me look at that again, then!

Answer 15

okie dokie

Answer 16

hmmm...hold on for a bit while I review. I cannot see any other way to solve this for x.

Answer 17

ok

Answer 18

Every place i look tells me the same thing...to take the common log of both sides. Let's ask @D3xt3R . He's really good with this. Maybe he can lend us his brain to get another way.

Answer 19

Logs exist because of these types of problems

Answer 20

;D ... Hello guys ;)

Answer 21

uh oh Solve 7.7^4x + 3 = 10.2

Answer 22

i typed the problem worng

Answer 23

help us to see the error in our ways, @D3xt3R !

Answer 24

oh my! You typed the problem wrong! I'm so glad to hear that cuz I thought I had gone stupid, or something! :/

Answer 25

my bad

Answer 26

Is\[7.7^{4x}+3=10.2~~or~~7.74^x+3=10.2???\]

Answer 27

That is so much better! Now the problem is this after we take the common log of both sides:\[4x \log (7.74)=\log (7.2)\]

Answer 28

4x = .96466

Answer 29

Now solve for x.

Answer 30

x = .24116

Answer 31

hmm...still off some

Answer 32

No matter what log do you chose, the result will be the same

Answer 33

\[ln(7.7^{4x})=ln(7.2)\]\[4x=\frac{ln(7.2)}{ln(7.7)}\]\[x=0.24178\]

Answer 34

see? it's not coming out right still

Answer 35

≈ -2.15
x ≈ -0.47
x ≈ 0.03
x ≈ 0.28

Answer 36

yeah??

Answer 37

Thinking

Answer 38

I got it ;)

Answer 39

whattt

Answer 40

\[7.7^{4x+3}=10.2\]\[ln(7.7^{4x+3})=ln(10.2)\]\[4x+3=\frac{ln(10.2)}{ln(7.7)}\]\[4x=1.134864-3\]\[4x=-1.865136\]\[x=-\frac{1.865136}{4}\]@IMStuck and @jonnyrco The correct answer is:\[\boxed{x\approx-0.47}\]

Answer 41

@IMStuck

Answer 42

thanks

Answer 43

aha those darn old exponents!

Answer 44

haha