Difficulty solving exponential equation \(\displaystyle{4}^{{x}}-{4}^{{1}}+{2}^{{x}}-{2}^{{1}}={\frac{{{5}}}{{{16}}}}\)

Ormezzani6cuu

Ormezzani6cuu

Answered question

2022-04-13

Difficulty solving exponential equation
4x41+2x21=516

Answer & Explanation

Ouhamiptkg

Ouhamiptkg

Beginner2022-04-14Added 18 answers

First, 41=4 and 21=2, so you can write it as 4x+2x6=516. Next, 4=22, so 4x=(22)x=22x=(2x)2. For convenience let y=2x; then you can rewrite the equation yet again as y2+y6=516, or y2+y10116=0. This is a straightforward quadratic equation in y; solve it to find y, then take logarithms to get logy=xlog2, so that x=logylog2

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