Logarithmic Stuff

Question

Can you solve for x in  this equations :

1/ log₃(√(x) + 2 ) = log₇x

 

Answer 1

No, I don't think so. Not a direct, or exact answer, at least. Not without using a graphical or recursive method, such as Newton's method or some other method.

 

What is the context of your question? If you are being tested on ways to find numerical solutions for algebraically "un-solvable" questions, we can use one of those methods.  If you are asking this in the context of a course topic in which there ought to be a way to solve for the answer, you may have mis-communicated this question.

 

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Edit:

You say that 49 was a correct answer.  It would be a correct answer if the log on the left did not appear to be the denominator of a fraction.

 

Apparently you meant this:

#1.       log₃(√(x) + 2) = log₇x

This is difficult to solve, but straight-forward to see that 49 does work as a solution.

 

but what you wrote means this:

1 ÷ (log₃(√(x) + 2)) = log₇x

This is really hard to solve, and 49 is definitely not a solution.

 

If your teacher's test was written so you thought the question was like I thought it was, explain this to your teacher .