SOLUTION: If 7^(2x)=3 What is the value of 7^(6x-1)?

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Question 972081: If 7^(2x)=3 What is the value of 7^(6x-1)?

Found 2 solutions by lwsshak3, ikleyn:
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
If 7^(2x)=3 What is the value of 7^(6x-1)?
***
2xlog7=log3
x=log3/2log7
..
7^(6x-1=7^(6log(3)/2log(7)-1)=1.5037...

Answer by ikleyn(53879) About Me  (Show Source):
You can put this solution on YOUR website!
.
If 7^(2x)=3 What is the value of 7^(6x-1)?
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        The answer in the post by @lwsshak3 is incorrect (numerically wrong),
        and the way how he solves the problem is not which is expected.

        A standard method is different. 


7%5E%286x-1%29 = %287%5E%286x%29%29%2F7 = %28%287%5E%282x%29%29%5E3%29%2F7 = now replace here 7%5E%282x%29 by 3, as it is given, and continue = 3%5E3%2F7 = 27%2F7 = 3.857142857 (approximately)


ANSWER.  The exact value is  27%2F7.  The decimal approximation is 3.857142857.

Solved correctly.

This way is what a teacher expects to get from a student - not the way which @lwsshak3 uses in his post.

For this problem and for many other similar problems the expected way is to build a chain of identities,
starting from the expression you want to evaluate and ending the exact numerical value, such that the given
equality is a link in this chain.