A Radical Logarithmic Equation

[@freddyalvaradamaranon304]

Interesante ejercicio ecuacion exponencial con logaritmos, muchas gracias por compartir tan buena explicación. 😊❤😊

[@rajkote29]

I love your videos you deserve a million subscribers

[@devondevon4366]

100 Answer x^log sqrt x = 100 square on both sides sqrt x ^ log x = 100 as a^log b = b^ log a as log 5 ^ log 6 = log 6^ log 5 log sqrt (x ) 100 = log x change from exponential form to log form Log x 10,000 = log x (square the base and the argument) as log 16/ log sqrt 4 = log 256 / log 4 log 10,000/ log x = log x / log 10 log 10,000 * log 10 = log x * log x cross multiply 4 = log x^2 4 = 2 log x 2 = log x divide both sides by 2 10^2 = x Answer change to exponential form 100 = x

[@yifengxiao]

simply use the properties of logarithm, log√x=(1/2)logx, then easily obtained (1/4)logx.logx=1(log10), it follows that logx=± 2.

[@stefanoskatharopoulos9173]

Since you asked which method I liked best, I can't saywhich. They were both grade.

[@roberttelarket4934]

It’s all about you SyberMath guy!

[@rakenzarnsworld2]

x = 10^2 or 10^(-2)

[@ilanbar1970]

I like more the 2nd method..

[@maxhagenauer24]

sqrt( x^log(sqrt(x)) ) = 10 => ( sqrt(x) )^log(sqrt(x)) = 10 y = sqrt(x) y^log(y) = 10 ( log(y) )^2 = 1 log(y) = ±1 y = 10, 1/10 10 = sqrt(x), 1/10 = sqrt(x) x = 100, 1/100

[@devondevon4366]

100

[@scottleung9587]

I also got 100 and 1/100.

[@trojanleo123]

x = 100 or x = 1/100

[@roberttelarket4934]

No it’s not my birthday.

[@prollysine]

sqrt(x^(log(x^(1/2))))=10 , ()^2 , x^(log(x^(1/2)))=100 , (log) , log(x^(1/2))*log(x)=log100 , / log100=2 / , (1/2)log(x)*log(x)=2 , (log(x))^2=4 , (sqrt) , log(x)=2 , / log -> only the positive result / , 10^(log(x))=10^2 , x=100 , / 10^(log(x))=x , / test , sqrt(100^(log(sqrt100))=sqrt(100^log(10)) , /log(10)=1 / , sqr((100)^1)=10 , same , OK ,