MyQuestionIcon

2

You visited us 2 times! Enjoying our articles? Unlock Full Access!

Property 6

Solve the fol...

Question

Solve the following equation:
$x^{{log}_{\sqrt{x}} (x - 2)} = 9$

Open in App

Solution

$_{x} {l o g}_{\sqrt{x}} (x - 2) = 9 \Rightarrow {(x - 2)}^{l o g x} \sqrt{x} = 9 \Rightarrow {(x - 2)}^{2} = 9 \Rightarrow x - 2 = 3$

Therefore, $x - 2 > 0$
$\Rightarrow x = 5$

Suggest Corrections

thumbs-up

0

Similar questions

Q. Solve the following equation:

\frac{1}{2} log x + 3 log \sqrt{2 + x} = log \sqrt{x (x + 2)} + 2

Q. Solve the following equation:

\frac{1}{2} {log}_{10} x + 3 {log}_{10} \sqrt{2 + x} = {log}_{10} \sqrt{x (x + 2)} + 2

Q. Solve the following quadratic equations by factorization:

\frac{x + 3}{x - 2} - \frac{1 - x}{x} = \frac{17}{4}

Q. Solve each of the following system of equations in R.

26.

\frac{|x + 2| - x}{x} < 2

Q. Solve the following equation and verify your answer:

\frac{x + 2}{x + 5} = \frac{x}{x + 6}

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Laws of Logarithm with Use

MATHEMATICS

Watch in App

explore_more_icon

Explore more

Standard IX Mathematics

Join BYJU'S Learning Program

CrossIcon