Math / Algebra

QuestionSolve the exponential equation. $4\left(10^{x}\right)=40,000$
Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution is $x=$ $\square$ (Simplify your answer. Use a comma to separate answers as needed.) B. There is no solution.

Studdy Solution

STEP 1

1. The equation $4(10^x) = 40,000$ is exponential.
2. We need to isolate the exponential term and solve for $x$ .

STEP 2

1. Isolate the exponential term $10^x$ .
2. Solve for $x$ by using logarithms or by equating powers of 10.

STEP 3

First, divide both sides of the equation by 4 to isolate the exponential term:
$4(10^x) = 40,000$ $10^x = \frac{40,000}{4}$ $10^x = 10,000$

STEP 4

Recognize that $10,000$ can be expressed as a power of 10. Specifically, $10,000 = 10^4$ .
$10^x = 10,000$ $10^x = 10^4$

STEP 5

Since the bases are the same, we can equate the exponents:
$x = 4$
The solution is: A. The solution is $x = 4$ .

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QuestionSolve the exponential equation. $4\left(10^{x}\right)=40,000$
Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution is $x=$ $\square$ (Simplify your answer. Use a comma to separate answers as needed.) B. There is no solution.

Studdy Solution

STEP 1

1. The equation $4(10^x) = 40,000$ is exponential.
2. We need to isolate the exponential term and solve for $x$ .

STEP 2

1. Isolate the exponential term $10^x$ .
2. Solve for $x$ by using logarithms or by equating powers of 10.

STEP 3

First, divide both sides of the equation by 4 to isolate the exponential term:
$4(10^x) = 40,000$ $10^x = \frac{40,000}{4}$ $10^x = 10,000$

STEP 4

Recognize that $10,000$ can be expressed as a power of 10. Specifically, $10,000 = 10^4$ .
$10^x = 10,000$ $10^x = 10^4$

STEP 5

Since the bases are the same, we can equate the exponents:
$x = 4$
The solution is: A. The solution is $x = 4$ .

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Studdy Solution

STEP 1

1. The equation 4(10x)=40,000 4(10^x) = 40,000 4(10x)=40,000 is exponential.2. We need to isolate the exponential term and solve for x x x.

STEP 2

1. Isolate the exponential term 10x 10^x 10x.2. Solve for x x x by using logarithms or by equating powers of 10.

STEP 3

First, divide both sides of the equation by 4 to isolate the exponential term:4(10x)=40,000 4(10^x) = 40,000 4(10x)=40,000 10x=40,0004 10^x = \frac{40,000}{4} 10x=440,000​ 10x=10,000 10^x = 10,000 10x=10,000

STEP 4

Recognize that 10,000 10,000 10,000 can be expressed as a power of 10. Specifically, 10,000=104 10,000 = 10^4 10,000=104.10x=10,000 10^x = 10,000 10x=10,000 10x=104 10^x = 10^4 10x=104

STEP 5

Since the bases are the same, we can equate the exponents:x=4 x = 4 x=4 The solution is: A. The solution is x=4 x = 4 x=4.

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1. The equation $4(10^x) = 40,000$ is exponential.
2. We need to isolate the exponential term and solve for $x$ .

1. Isolate the exponential term $10^x$ .
2. Solve for $x$ by using logarithms or by equating powers of 10.

First, divide both sides of the equation by 4 to isolate the exponential term:
$4(10^x) = 40,000$ $10^x = \frac{40,000}{4}$ $10^x = 10,000$

Recognize that $10,000$ can be expressed as a power of 10. Specifically, $10,000 = 10^4$ .
$10^x = 10,000$ $10^x = 10^4$

Since the bases are the same, we can equate the exponents:
$x = 4$
The solution is: A. The solution is $x = 4$ .