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Greatest Integer Function

Solve: 32x+9...

Question

Solve:
$3^{2 x} + 9 = 10 (3^{x})$

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Solution

Now,
$3^{2 x} + 9 = 10 (3^{x})$
or, $(3^{x})^{2} - 10 (3^{x}) + 9 = 0$
or, $(3^{x})^{2} - 3^{x} - {9.3}^{x} + 9 = 0$
or, $3^{x} (3^{x} - 1) - 9 (3^{x} - 1) = 0$
or, $(3^{x} - 1) (3^{x} - 9) = 0$
or, $3^{x} = 1$ or $3^{x} = 9$
or, $3^{x} = 3^{0}$ or $3^{x} = 3^{2}$
or, $x = 0$ or $x = 2$ .

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Similar questions

3^{2 x} + 9 = 10 (3^{x})

, then the value of

x^{2} + 1

3^{2 x} + {10.3}^{x} - 9 = 0

Q. Solve the following equations:

3^{2 x} + 9 = {10.3}^{x}

.

Q. Solve the following system of equations by matrix method:
(i) x + y − z = 3
2x + 3y + z = 10
3x − y − 7z = 1

(ii) x + y + z = 3
2x − y + z = − 1
2x + y − 3z = − 9

(iii) 6x − 12y + 25z = 4
4x + 15y − 20z = 3
2x + 18y + 15z = 10

(iv) 3x + 4y + 7z = 14
2x − y + 3z = 4
x + 2y − 3z = 0

(v)

\frac{2}{x} - \frac{3}{y} + \frac{3}{z} = 10 \frac{1}{x} + \frac{1}{y} + \frac{1}{z} = 10 \frac{3}{x} - \frac{1}{y} + \frac{2}{z} = 13

(vi) 5x + 3y + z = 16
2x + y + 3z = 19
x + 2y + 4z = 25

(vii) 3x + 4y + 2z = 8
2y − 3z = 3
x − 2y + 6z = −2

(viii) 2x + y + z = 2
x + 3y − z = 5
3x + y − 2z = 6

(ix) 2x + 6y = 2
3x − z = −8
2x − y + z = −3

(x) x − y + z = 2
2x − y = 0
2y − z = 1

(xi) 8x + 4y + 3z = 18
2x + y +z = 5
x + 2y + z = 5

(xii) x + y + z = 6
x + 2z = 7
3x + y + z = 12

(xiii)

\frac{2}{x} + \frac{3}{y} + \frac{10}{z} = 4, \frac{4}{x} - \frac{6}{y} + \frac{5}{z} = 1, \frac{6}{x} + \frac{9}{y} - \frac{20}{z} = 2; x, y, z \neq 0

(xiv) x − y + 2z = 7
3x + 4y − 5z = −5
2x − y + 3z = 12

\frac{2 x}{x - 3} + \frac{1}{2 x + 3} + \frac{3 x + 9}{(x - 3) (2 x + 3)} = 0

x + 1

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