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1 vote
Solve for x.
27=9^-x+5

2 Answers

4 votes
27=9^-x+5
3^3=3^2(-x+5)
3^3=3^(-2x+10)
3=-2x+10
X=7/2
Solve for x. 27=9^-x+5-example-1
User Billy Logan
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2 votes

We can rewrite 9^-x as (3^2)^-x, which is equal to 3^-2x. Then we have:

27 = 3^-2x + 5

Subtracting 5 from both sides gives:

22 = 3^-2x

Taking the reciprocal of both sides gives:

3^2x = 1/22

Taking the logarithm of both sides with base 3 gives:

2x = log₃(1/22)

Using the change of base formula, we get:

2x = log(1/22) / log(3)

Simplifying gives:

x = (1/2) * log(22) / log(3) - Answer

User Paul Morgan
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8.0k points

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