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IB Math Studies Exponential equations

Posted: Mon Apr 15, 2013 7:27 pm
IB Mathematical Studies SL – Algebra, Exponents, Indices, Exponential equations

How can we solve the following exponential equation?

$4^{x-7}=(\frac{1}{2})^{3-5x}$

Thanks

Re: IB Math Studies Exponential equations

Posted: Mon Apr 15, 2013 7:39 pm
IB Mathematical Studies SL – Algebra, Exponents, Indices, Exponential equations

In order to solve exponential equations we have to make the base numbers the same and then equate the indices.

$4^{x-7}=(\frac{1}{2})^{3-5x}$

$(2^2)^{x-7}=(2^{-1})^{3-5x}$

$2^{2(x-7)}= 2^{-(3-5x)}$

$2^{2x-14)}= 2^{-3+5x}$

$2x-14= -3+5x$

$3x=-11$

$x=\frac{-11}{3}$

Hope these help!!

Re: IB Math Studies Exponential equations

Posted: Mon Apr 15, 2013 7:42 pm
Thanks Elisabeth!!