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What is x equal to when 9^x = (1/3)^(x+3)?

User Mike The Tike
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2 Answers

16 votes
16 votes

Answer:

Explanation:

We can start solving this equation by taking the logarithm of both sides of the equation, using any base we prefer. Let's use the natural logarithm, denoted by "ln":

ln(9^x) = ln((1/3)^(x+3))

Using the rule that ln(a^b) = b*ln(a) for any positive real number a and any real number b, we can simplify the left-hand side:

x*ln(9) = (x+3)*ln(1/3)

Next, we can simplify the right-hand side using the rule that ln(1/a) = -ln(a) for any positive real number a:

x*ln(9) = -(x+3)*ln(3)

Now we can solve for x by isolating it on one side of the equation. First, let's simplify the logarithmic terms using the fact that ln(9) = 2*ln(3):

2x*ln(3) = -(x+3)*ln(3)

Dividing both sides of the equation by ln(3), we get:

2x = -(x+3)

Simplifying and solving for x, we obtain:

2x = -x - 3

3x = -3

x = -1

Therefore, the solution to the equation 9^x = (1/3)^(x+3) is x = -1.

User Annosz
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2.7k points
5 votes
5 votes

Answer: 1

Step-by-step explanation: x by itself is 1

User Duleshi
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2.8k points