Solved on Jan 19, 2024

Solve the exponential equation $3^{9x} = 3^{7x+8}$ for $x$ .

STEP 1

Assumptions
1. The equation to solve is $3^{9x} = 3^{7x+8}$ .
2. The base of the exponent on both sides of the equation is 3.
3. Since the bases are the same, the exponents must be equal for the equation to hold true.

STEP 2

Set the exponents equal to each other because the bases are the same and the equation can only be true if the exponents are equal.
$9x = 7x + 8$

STEP 3

Subtract $7x$ from both sides of the equation to isolate the variable $x$ on one side.
$9x - 7x = 7x + 8 - 7x$

STEP 4

Simplify the equation by combining like terms.
$2x = 8$

STEP 5

Divide both sides of the equation by 2 to solve for $x$ .
$\frac{2x}{2} = \frac{8}{2}$

STEP 6

Calculate the value of $x$ .
$x = 4$
The solution to the equation $3^{9x} = 3^{7x+8}$ is $x = 4$ .

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Solve the exponential equation $3^{9x} = 3^{7x+8}$ for $x$ .

STEP 1

Assumptions
1. The equation to solve is $3^{9x} = 3^{7x+8}$ .
2. The base of the exponent on both sides of the equation is 3.
3. Since the bases are the same, the exponents must be equal for the equation to hold true.

STEP 2

Set the exponents equal to each other because the bases are the same and the equation can only be true if the exponents are equal.
$9x = 7x + 8$

STEP 3

Subtract $7x$ from both sides of the equation to isolate the variable $x$ on one side.
$9x - 7x = 7x + 8 - 7x$

STEP 4

Simplify the equation by combining like terms.
$2x = 8$

STEP 5

Divide both sides of the equation by 2 to solve for $x$ .
$\frac{2x}{2} = \frac{8}{2}$

STEP 6

Calculate the value of $x$ .
$x = 4$
The solution to the equation $3^{9x} = 3^{7x+8}$ is $x = 4$ .

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Solve the exponential equation 39x=37x+83^{9x} = 3^{7x+8}39x=37x+8 for xxx.

STEP 1

Assumptions1. The equation to solve is 39x=37x+83^{9x} = 3^{7x+8}39x=37x+8.2. The base of the exponent on both sides of the equation is 3.3. Since the bases are the same, the exponents must be equal for the equation to hold true.

STEP 2

Set the exponents equal to each other because the bases are the same and the equation can only be true if the exponents are equal.9x=7x+89x = 7x + 89x=7x+8

STEP 3

Subtract 7x7x7x from both sides of the equation to isolate the variable xxx on one side.9x−7x=7x+8−7x9x - 7x = 7x + 8 - 7x9x−7x=7x+8−7x

STEP 4

Simplify the equation by combining like terms.2x=82x = 82x=8

STEP 5

Divide both sides of the equation by 2 to solve for xxx.2x2=82\frac{2x}{2} = \frac{8}{2}22x​=28​

STEP 6

Calculate the value of xxx.x=4x = 4x=4The solution to the equation 39x=37x+83^{9x} = 3^{7x+8}39x=37x+8 is x=4x = 4x=4.

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

Solve the exponential equation $3^{9x} = 3^{7x+8}$ for $x$ .

Assumptions
1. The equation to solve is $3^{9x} = 3^{7x+8}$ .
2. The base of the exponent on both sides of the equation is 3.
3. Since the bases are the same, the exponents must be equal for the equation to hold true.

Set the exponents equal to each other because the bases are the same and the equation can only be true if the exponents are equal.
$9x = 7x + 8$

Subtract $7x$ from both sides of the equation to isolate the variable $x$ on one side.
$9x - 7x = 7x + 8 - 7x$

Simplify the equation by combining like terms.
$2x = 8$

Divide both sides of the equation by 2 to solve for $x$ .
$\frac{2x}{2} = \frac{8}{2}$

Calculate the value of $x$ .
$x = 4$
The solution to the equation $3^{9x} = 3^{7x+8}$ is $x = 4$ .