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Question Number 34533 by tawa tawa last updated on 07/May/18

Solve for  x :               5 log_4 x   +   48 log_x 4    =    (x/8)

$$\mathrm{Solve}\:\mathrm{for}\:\:\mathrm{x}\::\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{5}\:\mathrm{log}_{\mathrm{4}} \mathrm{x}\:\:\:+\:\:\:\mathrm{48}\:\mathrm{log}_{\mathrm{x}} \mathrm{4}\:\:\:\:=\:\:\:\:\frac{\mathrm{x}}{\mathrm{8}} \\ $$

Commented by tawa tawa last updated on 08/May/18

yes sir.

$$\mathrm{yes}\:\mathrm{sir}. \\ $$

Commented by NECx last updated on 08/May/18

I remember those days when  Tawakalitu asked questions like  this.

$${I}\:{remember}\:{those}\:{days}\:{when} \\ $$$${Tawakalitu}\:{asked}\:{questions}\:{like} \\ $$$${this}. \\ $$

Commented by Rasheed.Sindhi last updated on 08/May/18

Once I thought that Tawakalitu and  Miss tawa tawa is same person....

$$\mathrm{Once}\:\mathrm{I}\:\mathrm{thought}\:\mathrm{that}\:{Tawakalitu}\:\mathrm{and} \\ $$$$\mathrm{Miss}\:\mathrm{tawa}\:\mathrm{tawa}\:\mathrm{is}\:\mathrm{same}\:\mathrm{person}.... \\ $$

Commented by tawa tawa last updated on 08/May/18

when i re install the app. it asked for new username. then i changed.

$$\mathrm{when}\:\mathrm{i}\:\mathrm{re}\:\mathrm{install}\:\mathrm{the}\:\mathrm{app}.\:\mathrm{it}\:\mathrm{asked}\:\mathrm{for}\:\mathrm{new}\:\mathrm{username}.\:\mathrm{then}\:\mathrm{i}\:\mathrm{changed}. \\ $$

Commented by Rasheed.Sindhi last updated on 10/May/18

THαnkS!

$$\mathcal{TH}\alpha{nk}\mathcal{S}! \\ $$

Answered by ajfour last updated on 08/May/18

x=256

$${x}=\mathrm{256} \\ $$

Answered by ajfour last updated on 08/May/18

5log _4 256 + 48log _(256) 4 =  5×4 + 48×(1/4) = 32 = ((256)/8)  .

$$\mathrm{5log}\:_{\mathrm{4}} \mathrm{256}\:+\:\mathrm{48log}\:_{\mathrm{256}} \mathrm{4}\:= \\ $$$$\mathrm{5}×\mathrm{4}\:+\:\mathrm{48}×\frac{\mathrm{1}}{\mathrm{4}}\:=\:\mathrm{32}\:=\:\frac{\mathrm{256}}{\mathrm{8}}\:\:. \\ $$

Commented by tawa tawa last updated on 08/May/18

No algebraic solution sir ?

$$\mathrm{No}\:\mathrm{algebraic}\:\mathrm{solution}\:\mathrm{sir}\:? \\ $$

Commented by ajfour last updated on 09/May/18

use the Wronskian . mrw sir  used to.

$${use}\:{the}\:{Wronskian}\:.\:{mrw}\:{sir} \\ $$$${used}\:{to}. \\ $$

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