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anonymous
 one year ago
Solve 3^(2x) = 7^(x−1).
anonymous
 one year ago
Solve 3^(2x) = 7^(x−1).

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\(\bf 3^{2x} = 7^{x1}\) right? for I don't see it happening

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0hmmm I assume you've covered logarithms?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0First step: Take the logarithm of both sides.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ao log 3^(2x)= log 7^(x1)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0OK. 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
 one year ago
Best ResponseYou've already chosen the best response.03^(2x) log= 7^(x1)= log

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[3^{2x}=7^{x1}=7^x*7^{1}\] \[\left( 3^2 \right)^x=\frac{ 7^x }{ 7 }\] \[\frac{ 9^x }{ 7^x }=\frac{ 1 }{ 7 }\] \[\left( \frac{ 9 }{ 7 } \right)^x=\frac{ 1 }{ 7 }\] take log and find x

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0−7.74293 7.74293 −1 1 These are the answer choices <3

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Not 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
 one year ago
Best ResponseYou've already chosen the best response.0Correct. Now do the same thing on the right hand side. You are trying to determine\[\log 7^{x1} = ?\]Applying the same rule, what do you get?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Not exactly. In this one, a = 7 and b = x1. Try again

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Backwards. Try again

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0i got 7.74293 as an answer

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0That's it. So now you done\[\log 3^{2x} = \log 7^{x1}\]\[2x \log 3 = \left( x1 \right) \log 7\]OK so far?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Great. Now expand the right hand side.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0That's the left hand side. You can multiply the 0.477... by the 2.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Excellent. The left hand side is 0.95424250944 x. Now, on to the left hand side. First thing to do is to expand it.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0** right hand side. Sorry

anonymous
 one year ago
Best ResponseYou've already chosen the best response.00.84509804001x0.845098804001

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Exactly 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
 one year ago
Best ResponseYou've already chosen the best response.00.36797678529=0.8450904001

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so would the answer be 7.74293?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Problem with the left hand side. Remember, you are subtracting 0.84509804001 x from both sides. Try the left hand side again.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0That'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
 one year ago
Best ResponseYou've already chosen the best response.0Yayyyy! If I post another question in the open section, will u answer?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0To avoid dealing with all those decimal places, most folks will leave the logs until the end, for example\[2x \log 3 = (x1)\log 7\]\[(2 \log 3) x = (\log 7) x  \log 7\]\[(2 \log 3  \log 7) x = \log 7\]\[x = \frac{ \log 7 }{ 2 \log 3  \log 7 }\]Then plug it into your calculator
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