Question

x^√x=(√x)^x,solve it​

Answer 1

Solution

$x {}^{ \sqrt{x} } = (\sqrt{x} ) {}^{x} \\ = > x {}^{ \sqrt{x} } = x {}^{ \frac{x}{2} } \\ = > \sqrt{x} = \frac{x}{2} \\ = > x = \frac{x {}^{2} }{4} \\ = > x(1 - \frac{x}{4} ) = 0 \\ = > either....x = 0 \\ or......1 - \frac{x}{4} = 0 = > x = 4$

Hope this helps you......

Answer 2

Answer:

x = 4

Step-by-step explanation:

x^√x=(√x)^x

Introducing log to both sides

log(x^√x)=log{(√x)^x}

√xlogx = xlog√x

So that;

(√x)/x = (log√x)/logx  

1/√x = (log√x)/logx  

Cross multiply to get;

logx/√x = log√x

logx = √x log√x

logx = log√x^(√x)

logx = logx^(√x/2)

Now remove the log

x = x^(√x/2)

x^1 = x^(√x/2)

1 = √x/2

√x = 2

: . x = 4