QuestionSolve $(\sqrt{3})^{x} \cdot(\sqrt{2})^{x}=36$ for $x$ : (a) 1 (b) 2 (c) 3 (d) 4 (e) None.

Studdy Solution

STEP 1

Assumptions1. We are given the equation $(\sqrt{3})^{x} \cdot(\sqrt{})^{x}=36$ . We need to find the value of $x$
3. The possible values of $x$ are given as1,,3,4, or none of these

STEP 2

First, we need to rewrite the equation in a more manageable form. We can do this by combining the two terms on the left side of the equation into a single term.
$(\sqrt{})^{x} \cdot(\sqrt{2})^{x} = (\sqrt{} \cdot \sqrt{2})^{x}$

STEP 3

Now, simplify the equation by multiplying the square roots.
$(\sqrt{3} \cdot \sqrt{2})^{x} = (\sqrt{6})^{x}$

STEP 4

We can rewrite the equation in exponential form.
$(\sqrt{6})^{x} =36$

STEP 5

We know that $\sqrt{}^2 =$ , so we can rewrite the equation as $^{x} =36$

STEP 6

We can rewrite the right side of the equation as $6^2$ to match the base on the left side.
$6^{x} =6^{2}$

STEP 7

Now, we can equate the exponents, as the bases are the same.
$x =2$ So, the value of $x$ is2.

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QuestionSolve $(\sqrt{3})^{x} \cdot(\sqrt{2})^{x}=36$ for $x$ : (a) 1 (b) 2 (c) 3 (d) 4 (e) None.

Studdy Solution

STEP 1

Assumptions1. We are given the equation $(\sqrt{3})^{x} \cdot(\sqrt{})^{x}=36$ . We need to find the value of $x$
3. The possible values of $x$ are given as1,,3,4, or none of these

STEP 2

First, we need to rewrite the equation in a more manageable form. We can do this by combining the two terms on the left side of the equation into a single term.
$(\sqrt{})^{x} \cdot(\sqrt{2})^{x} = (\sqrt{} \cdot \sqrt{2})^{x}$

STEP 3

Now, simplify the equation by multiplying the square roots.
$(\sqrt{3} \cdot \sqrt{2})^{x} = (\sqrt{6})^{x}$

STEP 4

We can rewrite the equation in exponential form.
$(\sqrt{6})^{x} =36$

STEP 5

We know that $\sqrt{}^2 =$ , so we can rewrite the equation as $^{x} =36$

STEP 6

We can rewrite the right side of the equation as $6^2$ to match the base on the left side.
$6^{x} =6^{2}$

STEP 7

Now, we can equate the exponents, as the bases are the same.
$x =2$ So, the value of $x$ is2.

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QuestionSolve (3)x⋅(2)x=36(\sqrt{3})^{x} \cdot(\sqrt{2})^{x}=36(3​)x⋅(2​)x=36 for xxx: (a) 1 (b) 2 (c) 3 (d) 4 (e) None.

Studdy Solution

STEP 1

Assumptions1. We are given the equation (3)x⋅()x=36(\sqrt{3})^{x} \cdot(\sqrt{})^{x}=36(3​)x⋅(​)x=36 . We need to find the value of xxx3. The possible values of xxx are given as1,,3,4, or none of these

STEP 2

First, we need to rewrite the equation in a more manageable form. We can do this by combining the two terms on the left side of the equation into a single term.()x⋅(2)x=(⋅2)x (\sqrt{})^{x} \cdot(\sqrt{2})^{x} = (\sqrt{} \cdot \sqrt{2})^{x} (​)x⋅(2​)x=(​⋅2​)x

STEP 3

Now, simplify the equation by multiplying the square roots.(3⋅2)x=(6)x (\sqrt{3} \cdot \sqrt{2})^{x} = (\sqrt{6})^{x} (3​⋅2​)x=(6​)x

STEP 4

We can rewrite the equation in exponential form.(6)x=36 (\sqrt{6})^{x} =36 (6​)x=36

STEP 5

We know that 2=\sqrt{}^2 =​2=, so we can rewrite the equation asx=36^{x} =36 x=36

STEP 6

We can rewrite the right side of the equation as 626^262 to match the base on the left side.6x=626^{x} =6^{2} 6x=62

STEP 7

Now, we can equate the exponents, as the bases are the same.x=2 x =2 x=2So, the value of xxx is2.

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Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionSolve $(\sqrt{3})^{x} \cdot(\sqrt{2})^{x}=36$ for $x$ : (a) 1 (b) 2 (c) 3 (d) 4 (e) None.

Assumptions1. We are given the equation $(\sqrt{3})^{x} \cdot(\sqrt{})^{x}=36$ . We need to find the value of $x$
3. The possible values of $x$ are given as1,,3,4, or none of these

First, we need to rewrite the equation in a more manageable form. We can do this by combining the two terms on the left side of the equation into a single term.
$(\sqrt{})^{x} \cdot(\sqrt{2})^{x} = (\sqrt{} \cdot \sqrt{2})^{x}$

Now, simplify the equation by multiplying the square roots.
$(\sqrt{3} \cdot \sqrt{2})^{x} = (\sqrt{6})^{x}$

We can rewrite the equation in exponential form.
$(\sqrt{6})^{x} =36$

We know that $\sqrt{}^2 =$ , so we can rewrite the equation as $^{x} =36$

We can rewrite the right side of the equation as $6^2$ to match the base on the left side.
$6^{x} =6^{2}$

Now, we can equate the exponents, as the bases are the same.
$x =2$ So, the value of $x$ is2.