Question

Solve the given equation.
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Answer 1

Answer:

x = 5

Step-by-step explanation:

Formula used:

$a^{log_{a}N}=N$

$x^{log_{\sqrt{x}}(x-2)}=9$

$(x^{\frac{1}{2}})^{2\:log_{\sqrt{x}}(x-2)}=9$

$({\sqrt{x}})^{2\:log_{\sqrt{x}}(x-2)}=9$

${\sqrt{x}}^{log_{\sqrt{x}}(x-2)^2}=9$ (using the given formula)

$(x-2)^2=9$

$x-2=$±$3$

$x=2$±$3$

x=5, -1

But x cannot be negative

x= 5