SOLUTION: log5x = 2-logx5

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Question 324723: log5x = 2-logx5
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


I'm presuming you mean:



And that you want to solve the equation for

To the extent that is all true, please remember the following things for the next time you post.

1. The proper way to render on the standard keyboard is log_b(x).

2. Take the time to tell us what it is you want. Just putting in a problem and not saying anything else sends a very strong message, to wit: "Here chump, go do my homework for me. I've got more important things to occupy my time, like video games or hanging out at the mall." That sort of thing is not very conducive to getting someone to help you.

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First, convert the base of the log function in the RHS to the same base as the log function in the LHS:

Use the log base conversion formula:



So:



But since



we now have:



Put everything into the LHS:



Multiply both sides by



Let and substitute:



Factor:



Hence:



Substitute back:



Use the definition of the log function:



Hence:



Which is to say:



Check:



Checks!

John