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Hi everyone,
This forum provides such excellent help that I am back.
This time I am attempting to solve basic logarithmic equations. As I was working my way through the questions, a couple of them stumped me.
Here they are:
Solve for x:
1) 5 logx (625) = 10
2) -log3x -1 (1/32) = 5
So, x, and 3x -1 are the respective bases of the logarithm in the above examples. In the first question, I started by dividing both sides by "5" to get logx 625 = 2. And then I simplified to get 4 logx 5 = 2. I divided both sides by 4 again and achieved: logx 5 = 2/4 = 1/2
But from there I am not sure how to go. And I was on an utterly wrong tangent for question 2.
Any help at all will be much appreciated!
Thanks,
Nathaniel
Thank you so much, Prove It!
Also, two more things: with the first equation, when you reach logx 25 = 1, why is it that no further simplification takes place upon the 25 numeral? I know x = 25 is the correct answer, but I am just curious as to why no further simplification takes place.
In the second equation, how come you don't divide 5 by -1 to yield -5?
Cheers,
Nathaniel
He could have said so that but does that really simplify anything?
leads to 25= x^1 and leads to 5= x^{1/2} which then gives x= 25.
The crucial point is: if and only if .
If you divide both sides of by -5, you get which (again changing to becomes and probably the best thing to do would be to recognize that so that .In the second equation, how come you don't divide 5 by -1 to yield -5?
Instead, seeing that there was already a fraction inside the logarithm, Prove It chose to use the law of logarithms, taking the -1 inside the logarithm to "cancel" that fraction:
Once again, the crucial point for all these problems is that is exactly the same as .
Cheers,
Nathaniel