Question Solve the exponential equation $3^{x}=81$ .

Studdy Solution

STEP 1

Assumptions
1. We are given the equation $3^{x} = 81$ .
2. We need to solve for the value of $x$ .

STEP 2

Recognize that $81$ is a power of $3$ , since $81 = 3^4$ .

STEP 3

Rewrite the equation using $81$ as a power of $3$ .
$3^{x} = 3^4$

STEP 4

Since the bases are the same and the equation states that the two expressions are equal, the exponents must also be equal.

STEP 5

Set the exponents equal to each other to solve for $x$ .
$x = 4$
The solution to the equation $3^{x} = 81$ is $x = 4$ .

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Question Solve the exponential equation $3^{x}=81$ .

Studdy Solution

STEP 1

Assumptions
1. We are given the equation $3^{x} = 81$ .
2. We need to solve for the value of $x$ .

STEP 2

Recognize that $81$ is a power of $3$ , since $81 = 3^4$ .

STEP 3

Rewrite the equation using $81$ as a power of $3$ .
$3^{x} = 3^4$

STEP 4

Since the bases are the same and the equation states that the two expressions are equal, the exponents must also be equal.

STEP 5

Set the exponents equal to each other to solve for $x$ .
$x = 4$
The solution to the equation $3^{x} = 81$ is $x = 4$ .

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Question Solve the exponential equation 3x=813^{x}=813x=81.

Studdy Solution

STEP 1

Assumptions1. We are given the equation 3x=813^{x} = 813x=81.2. We need to solve for the value of xxx.

STEP 2

Recognize that 818181 is a power of 333, since 81=3481 = 3^481=34.

STEP 3

Rewrite the equation using 818181 as a power of 333.3x=343^{x} = 3^43x=34

STEP 4

Since the bases are the same and the equation states that the two expressions are equal, the exponents must also be equal.

STEP 5

Set the exponents equal to each other to solve for xxx.x=4x = 4x=4The solution to the equation 3x=813^{x} = 813x=81 is x=4x = 4x=4.

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Studdy solves anything!

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Question Solve the exponential equation $3^{x}=81$ .

Assumptions
1. We are given the equation $3^{x} = 81$ .
2. We need to solve for the value of $x$ .

Recognize that $81$ is a power of $3$ , since $81 = 3^4$ .

Rewrite the equation using $81$ as a power of $3$ .
$3^{x} = 3^4$

Set the exponents equal to each other to solve for $x$ .
$x = 4$
The solution to the equation $3^{x} = 81$ is $x = 4$ .