Question

Solve 3^(2x) = 7^(x−1).

Answer 1

hellpp

Answer 2

\(\bf 3^{2x} = 7^{x-1}\) right?
for I don't see it happening

Answer 3

yes @jdoe0001

Answer 4

hmmm

Answer 5

hmm hold the mayo

Answer 6

kk

Answer 7

@Michele_Laino

Answer 8

hmmm I assume you've covered logarithms?

Answer 9

First step: Take the logarithm of both sides.

Answer 10

ao log 3^(2x)= log 7^(x-1)

Answer 11

hello?

Answer 12

OK. When you have a power, the way to take the log is as follows:\[\log a ^{b} = b \log a\]For example\[\log 5^\left( x+2 \right) = \left( x+2 \right) \log 5\] Try this with your question

Answer 13

3^(2x) log= 7^(x-1)= log

Answer 14

\[3^{2x}=7^{x-1}=7^x*7^{-1}\]
\[\left( 3^2 \right)^x=\frac{ 7^x }{ 7 }\]
\[\frac{ 9^x }{ 7^x }=\frac{ 1 }{ 7 }\]
\[\left( \frac{ 9 }{ 7 } \right)^x=\frac{ 1 }{ 7 }\]
take log and find x

Answer 15

−7.74293
7.74293
−1
1
These are the answer choices <3

Answer 16

Not quite. Let's look at just the left hand side. You are trying to determine\[\log 3^{2x} = ?\]Compare that with the general case\[\log a^b = b \log a\]Substitute a = 3 and b = 2x. What do you get?

Answer 17

2x log 3

Answer 18

was i right

Answer 19

Correct. Now do the same thing on the right hand side. You are trying to determine\[\log 7^{x-1} = ?\]Applying the same rule, what do you get?

Answer 20

x-1=log 7

Answer 21

yes?

Answer 22

Not exactly. In this one, a = 7 and b = x-1. Try again

Answer 23

7 log x-1

Answer 24

Backwards. Try again

Answer 25

x-1 log 7??

Answer 26

i got -7.74293 as an answer

Answer 27

That's it. So now you done\[\log 3^{2x} = \log 7^{x-1}\]\[2x \log 3 = \left( x-1 \right) \log 7\]OK so far?

Answer 28

yes! I am good

Answer 29

Great. Now expand the right hand side.

Answer 30

0.47712125472(2x)

Answer 31

That's the left hand side. You can multiply the 0.477... by the 2.

Answer 32

0.95424250943 sorry

Answer 33

Excellent. The left hand side is 0.95424250944 x. Now, on to the left hand side. First thing to do is to expand it.

Answer 34

** right hand side. Sorry

Answer 35

0.84509804001x-0.845098804001

Answer 36

right??

Answer 37

Exactly well done! So now you have\[0.95424250944 x = 0.84509804001 x - 0.8450904001\]Can you gather up the x's on one side and solve?

Answer 38

-0.36797678529=-0.8450904001

Answer 39

so would the answer be 7.74293?

Answer 40

Problem with the left hand side. Remember, you are subtracting 0.84509804001 x from both sides. Try the left hand side again.

Answer 41

0.10914370543x

Answer 42

That's better. So you have\[0.10914370543 x = 0.84509804001\]To solve for x, divide both sides by 0.10914370543. What do you get?

Answer 43

7.74298468868
!!!!

Answer 44

Yayyyy!! Well done!

Answer 45

Yayyyy! If I post another question in the open section, will u answer?

Answer 46

thanks:)

Answer 47

Yup. You're welcome

Answer 48

To avoid dealing with all those decimal places, most folks will leave the logs until the end, for example\[2x \log 3 = (x-1)\log 7\]\[(2 \log 3) x = (\log 7) x - \log 7\]\[(2 \log 3 - \log 7) x = -\log 7\]\[x = \frac{ -\log 7 }{ 2 \log 3 - \log 7 }\]Then plug it into your calculator