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0.7^x*0.3^x=0.1
We move all terms to the left:
0.7^x*0.3^x-(0.1)=0
We add all the numbers together, and all the variables
0.7^x*0.3^x-0.1=0
We move all terms containing x to the left, all other terms to the right
0.7^x*0.3^x=0.1
x=0.1/1
x=0.1
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