Solve-for-real-x-

Question Number 204742 by York12 last updated on 26/Feb/24

Solve for real x

Commented by York12 last updated on 26/Feb/24

Commented by TonyCWX08 last updated on 27/Feb/24

x \approx 0.933361

Commented by Ghisom last updated on 27/Feb/24

using intuition because {it}^{'} s not exactly

solveable if {there}^{'} s no easy solution

both sides 3^{something}

rhs would be nice if x had factors 2^{p} 7^{q}

\log_{7} \frac{2^{p / 16} 7^{q / 16}}{2^{1 / 4}} = \log_{7} (2^{(p - 4) / 16}) + q

very nice if p = 4 and q = \pm 3 \Rightarrow

\Rightarrow rhs = \sqrt{3} or rhs = \frac{\sqrt{3}}{3}

now try x = 2^{4} 7^{3} or x = 2^{4} 7^{- 3} in lhs

\Rightarrow

x = 2^{4} 7^{- 3} = \frac{16}{343}

Commented by York12 last updated on 27/Feb/24

thank you

Answered by Ghisom last updated on 27/Feb/24

x = \frac{16}{343}

Commented by York12 last updated on 27/Feb/24

Can you provide solution please

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