solve log equation: ab^x = c

Quadratic equations and inequalities, variation equations, function notation, systems of equations, etc.
santaclaus
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solve log equation: ab^x = c

Postby santaclaus » Mon Apr 13, 2009 7:16 am

so, abx=c

do I just say that a * x log b=c and solve for x?
and then x=c/a * log b? and that's the answer?

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stapel_eliz
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Postby stapel_eliz » Mon Apr 13, 2009 11:05 am

santaclaus wrote:so, abx=c

do I just say that a * x log b=c and solve for x?

Just as you cannot take the square root of only one factor of one term in an equation, while leaving the others unaffected; just as you cannot divide only one term in an equation, while leaving the others unaffected; just as you cannot square only one portion of an expression in an equation, while leaving the rest unaffected; just as you've always had to do the same thing to both sides of a given equation, so also you must "log" both sides of an exponential equation.

To learn the basics of solving exponential equations, please study this lesson.

Thank you! :D

santaclaus
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Re: solve log equation: ab^x = c

Postby santaclaus » Mon Apr 13, 2009 11:51 am

ok, so after taking log of both sides, sorry, I meant to do that, do I solve for x?
a * x log b=log c and solve for x?
so x=log c/log b?

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stapel_eliz
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Postby stapel_eliz » Mon Apr 13, 2009 7:37 pm

santaclaus wrote:ok, so after taking log of both sides...
a * x log b=log c and solve for x?

The only way you could arrive at the above equation would be to take the log, on the left, of the bx only. You cannot take the log of just one of the factors of the term. You must take the log of the entire side.

The lesson in the link (provided earlier) will explain this further. :wink:


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