Question Number 202813 by pascal889 last updated on 03/Jan/24
$$\left(\boldsymbol{\mathrm{x}}\:+\:\mathrm{1}\right)^{\boldsymbol{\mathrm{x}}} \:\:=\:\mathrm{625} \\ $$$$\boldsymbol{\mathrm{solve}}\:\boldsymbol{\mathrm{for}}\:\boldsymbol{\mathrm{x}} \\ $$$$ \\ $$
Commented by mr W last updated on 03/Jan/24
$$\mathrm{625}=\mathrm{25}×\mathrm{25}=\mathrm{5}^{\mathrm{2}} ×\mathrm{5}^{\mathrm{2}} =\mathrm{5}^{\mathrm{4}} =\left(\mathrm{4}+\mathrm{1}\right)^{\mathrm{4}} \\ $$$${x}=\mathrm{4} \\ $$$${x}\approx−\mathrm{0}.\mathrm{9984162559350108} \\ $$
Commented by mr W last updated on 04/Jan/24
$${generaly}\:{we}\:{can}\:{only}\:{approximate}. \\ $$$${let}\:{x}=−{u} \\ $$$$\left(−{u}+\mathrm{1}\right)^{−{u}} =\mathrm{625} \\ $$$$\Rightarrow\left(\mathrm{1}−{u}\right)^{{u}} −\frac{\mathrm{1}}{\mathrm{625}}=\mathrm{0} \\ $$
Commented by mr W last updated on 04/Jan/24
Commented by MathematicalUser2357 last updated on 05/Jan/24
$$\mathrm{Q}.\mathrm{202352} \\ $$$$“\mathrm{What}\:\mathrm{the}\:\mathrm{limit}\:\mathrm{is}\:\mathrm{grapher}?'' \\ $$
Commented by mr W last updated on 05/Jan/24
$${what}\:{do}\:{you}\:{want}\:{to}\:{know}\:{exactly}? \\ $$$${what}\:{do}\:{you}\:{mean}\:{with}\:“{the}\:{limit}''? \\ $$
Commented by MathematicalUser2357 last updated on 06/Jan/24
$$\mathrm{there}'\mathrm{s}\:\mathrm{no}\:\mathrm{app} \\ $$
Commented by mr W last updated on 06/Jan/24
$${where}\:{there}\:{is}\:{no}\:{app}?\:{the}\:{screen} \\ $$$${shot}\:{above}\:{shows}\:{the}\:{app}\:{in}\:{google} \\ $$$${app}\:{store}. \\ $$
Commented by MathematicalUser2357 last updated on 06/Jan/24
$$\mathrm{Ignore}\:“\mathrm{the}\:\mathrm{limit}''. \\ $$
Commented by mr W last updated on 06/Jan/24
$${a}\:{powerful}\:{app}\:{for}\:{graphing} \\ $$$${mathematical}\:{functions}… \\ $$
Commented by mr W last updated on 06/Jan/24
Commented by MathematicalUser2357 last updated on 06/Jan/24
$$\mathrm{IT}\:\mathrm{SAYS}\:\mathrm{CANNOT}\:\mathrm{DOWNLOAD}\:\mathrm{ON}\:\mathrm{DEVICES} \\ $$
Commented by MathematicalUser2357 last updated on 06/Jan/24
Commented by MathematicalUser2357 last updated on 06/Jan/24
$$\mathrm{I}\:\mathrm{CAN}'\mathrm{T}\:\mathrm{DOWNLOAD} \\ $$
Commented by mr W last updated on 06/Jan/24
$${i}\:{can}'{t}\:{help}\:{you}\:{that}\:{you}\:{have}\:{problem} \\ $$$${with}\:{the}\:{download}. \\ $$