hello-please-someone-help-me-to-correct-the-equation-It-s-typed-wrong-and-I-can-t-find-where-Solve-5-76-log-a-log-b-a-log-log-a-log-log-a-2-log-2-x-1-5-

Question Number 175040 by andres_chu last updated on 17/Aug/22

hello, please, someone help me to correct the equation? It's typed wrong and I can't find where

S o l v e :

5, 76 [\frac{\log_{a} (\sqrt{\log_{b} (\sqrt{a})})}{\log (\sqrt{\log (a)})} + \log_{\log (a)} (2)] \sqrt[5]{\log_{2} (x)} + \frac{\log_{2} (x)}{25} = {[\log_{2} (x)]}^{\frac{3}{5}}

A n s w e r s

x_{1} = 1, x_{2} = 2^{243}, x_{3} = 2^{- 243}, x_{4} = 2^{1024}, x_{5} = 2^{- 1024}

Answered by a.lgnaoui last updated on 20/Aug/22

t h e e q u a t i o n w i l l b e :

5, 76 [\frac{\log (\sqrt{\log (\sqrt{(a)}}}{\log (\sqrt{\log (a)}} + \log_{\log (a)} (2)] {(\log {(x)}_{2})}^{1 / 5} + \frac{\log_{2} (x)}{25} = {(\log_{2} (x))}^{3 / 5}

\frac{\log (\sqrt{\log (\sqrt{a))}}}{\log (\sqrt{\log (a)}} + \log_{\log (a)} (2) = [\frac{\frac{1}{2} \log (\frac{1}{2} \log (a))}{\frac{1}{2} \log (\log (a))} + \frac{\log (2)}{\log (\log (a))}]

\frac{\log (\log (a)) - \log (2)}{\log (\log (a))} + \frac{\log (2)}{\log (\log (a))} = 1

5, 76 {(\log_{2} x)}^{1 / 5} + \frac{\log_{2} (x)}{25} = {(\log_{2} (x))}^{3 / 5}

posons {(\log_{2} (x))}^{1 / 5} = X

X [5, 76 + \frac{X^{4}}{25} - X^{2} = 0] \Rightarrow X^{4} - {25 X}^{2} + 144 = 0

Z = X^{2} Z^{2} - 25 Z + 144 = 0 Δ = 7^{2} Z = \frac{25 \pm 7}{2} = (9, 16) X = (3, 4)

{[\log_{2} (x)]}^{1 / 5} = 3 \Rightarrow \log (x) = 3^{5} \log {(2)}^{5} x = 7, 68 \times 10^{16}

x = 4 \log_{2} (x) = 4^{5} [\log (x) = 4^{5} \log {(2)}^{5} x = 1, 428 \times 10^{71}