Substitution with logarithmic functions

label Algebra
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I asked this question earlier: find x for log₂(4.3ˣ-6)-log₂(9ˣ-6)=1

I understand the first part, but do not understand the substitution.

Can someone please thoroughly explain the steps after let u=3ˣ ?

Please and thank you

Dec 9th, 2014

Because 9^x = (3^2)^x, when we substitute 3^x as u , 9^x will become u^2

3x =u

9x = (32)x = 32x = (3x)2 = u2

I hope this will make you understand how we can get the quadratic equation in u


Dec 9th, 2014

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Dec 9th, 2014
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Dec 9th, 2014
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