solve the following equation:
[math] x^{x^4}=64[/math] in real Nos
Put [math]x^4=y[/math] ,then [math]y^y= (x^4)^{x^4}=(x^{x^4})^4=64^4=2^{24}[/math]
And taking logs we have :[math]ylog_2{y}=24[/math] which implies that y=8
And hence [math]x=2^\frac{3}{4}[/math] or [math]x=-2^\frac{3}{4}[/math]
Is that correct?
[math] x^{x^4}=64[/math] in real Nos
Put [math]x^4=y[/math] ,then [math]y^y= (x^4)^{x^4}=(x^{x^4})^4=64^4=2^{24}[/math]
And taking logs we have :[math]ylog_2{y}=24[/math] which implies that y=8
And hence [math]x=2^\frac{3}{4}[/math] or [math]x=-2^\frac{3}{4}[/math]
Is that correct?