anonymous
  • anonymous
Solve 3^(2x) = 7^(x−1).
Mathematics
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
chestercat
  • chestercat
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
anonymous
  • anonymous
hellpp
jdoe0001
  • jdoe0001
\(\bf 3^{2x} = 7^{x-1}\) right? for I don't see it happening
anonymous
  • anonymous
yes @jdoe0001

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

jdoe0001
  • jdoe0001
hmmm
jdoe0001
  • jdoe0001
hmm hold the mayo
anonymous
  • anonymous
kk
anonymous
  • anonymous
@Michele_Laino
jdoe0001
  • jdoe0001
hmmm I assume you've covered logarithms?
anonymous
  • anonymous
First step: Take the logarithm of both sides.
anonymous
  • anonymous
ao log 3^(2x)= log 7^(x-1)
anonymous
  • anonymous
hello?
anonymous
  • anonymous
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
anonymous
  • anonymous
3^(2x) log= 7^(x-1)= log
anonymous
  • anonymous
\[3^{2x}=7^{x-1}=7^x*7^{-1}\] \[\left( 3^2 \right)^x=\frac{ 7^x }{ 7 }\] \[\frac{ 9^x }{ 7^x }=\frac{ 1 }{ 7 }\] \[\left( \frac{ 9 }{ 7 } \right)^x=\frac{ 1 }{ 7 }\] take log and find x
anonymous
  • anonymous
−7.74293 7.74293 −1 1 These are the answer choices <3
anonymous
  • anonymous
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?
anonymous
  • anonymous
2x log 3
anonymous
  • anonymous
was i right
anonymous
  • anonymous
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?
anonymous
  • anonymous
x-1=log 7
anonymous
  • anonymous
yes?
anonymous
  • anonymous
Not exactly. In this one, a = 7 and b = x-1. Try again
anonymous
  • anonymous
7 log x-1
anonymous
  • anonymous
Backwards. Try again
anonymous
  • anonymous
x-1 log 7??
anonymous
  • anonymous
i got -7.74293 as an answer
anonymous
  • anonymous
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?
anonymous
  • anonymous
yes! I am good
anonymous
  • anonymous
Great. Now expand the right hand side.
anonymous
  • anonymous
0.47712125472(2x)
anonymous
  • anonymous
That's the left hand side. You can multiply the 0.477... by the 2.
anonymous
  • anonymous
0.95424250943 sorry
anonymous
  • anonymous
Excellent. The left hand side is 0.95424250944 x. Now, on to the left hand side. First thing to do is to expand it.
anonymous
  • anonymous
** right hand side. Sorry
anonymous
  • anonymous
0.84509804001x-0.845098804001
anonymous
  • anonymous
right??
anonymous
  • anonymous
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?
anonymous
  • anonymous
-0.36797678529=-0.8450904001
anonymous
  • anonymous
so would the answer be 7.74293?
anonymous
  • anonymous
Problem with the left hand side. Remember, you are subtracting 0.84509804001 x from both sides. Try the left hand side again.
anonymous
  • anonymous
0.10914370543x
anonymous
  • anonymous
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?
anonymous
  • anonymous
7.74298468868 !!!!
anonymous
  • anonymous
Yayyyy!! Well done!
anonymous
  • anonymous
Yayyyy! If I post another question in the open section, will u answer?
anonymous
  • anonymous
thanks:)
anonymous
  • anonymous
Yup. You're welcome
anonymous
  • anonymous
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

Looking for something else?

Not the answer you are looking for? Search for more explanations.