1. If $$9^{x-\frac{1}{2}}-2^{2x-2}=4^{x}-3^{2x-3}$$, then $$x$$ is
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By: anil on 05 May 2019 03.31 am
It is given that $$9^{x-frac{1}{2}}-2^{2x-2}=4^{x}-3^{2x-3}$$ Let us try to reduce them to powers of $$3$$ and $$2$$
The given equation can be reduced to $$3^{2x-1} + 3^{2x-3} = 2^{2x} + 2^{2x-2}$$
Hence, $$3^{2x-3} imes 10 = 2^{2x-2} imes 5$$
Therefore, $$3^{2x-3} = 2^{2x-3}$$ This is possible only if $$2x-3=0$$ or $$x=3/2$$
By: anil on 05 May 2019 03.31 am
It is given that $$9^{x-frac{1}{2}}-2^{2x-2}=4^{x}-3^{2x-3}$$ Let us try to reduce them to powers of $$3$$ and $$2$$
The given equation can be reduced to $$3^{2x-1} + 3^{2x-3} = 2^{2x} + 2^{2x-2}$$
Hence, $$3^{2x-3} imes 10 = 2^{2x-2} imes 5$$
Therefore, $$3^{2x-3} = 2^{2x-3}$$ This is possible only if $$2x-3=0$$ or $$x=3/2$$
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The given equation can be reduced to $$3^{2x-1} + 3^{2x-3} = 2^{2x} + 2^{2x-2}$$
Hence, $$3^{2x-3} imes 10 = 2^{2x-2} imes 5$$
Therefore, $$3^{2x-3} = 2^{2x-3}$$ This is possible only if $$2x-3=0$$ or $$x=3/2$$