Question

Solve for x. 3^x−1=9^x+2 Enter your answer in the box. x =

Answer 1

The solution is x = -5

Step-by-step explanation:

Given equation is:

$3^{(x-1)} = 9^{(x+2)}$

In order to solve the eponnetial equations, we have to equate the bases of both sides so that the exponents can be put equal

So,

Replacing 9 with 3^2

$3^{(x-1)} = (3^2)^{(x+2)}$

When there are exponents on exponents, both are multiplied so,

$3^{(x-1)} = 3^{(2x+4)}$

As the bases on both sides are same, the exponents can be put equal

So,

$x-1 = 2x+4$

Adding 1 on both sides

$x-1+1 = 2x+4+1\\x = 2x+5$

Subtracting 2x from both sides

$x-2x = 2x-2x+5\\-x = 5\\x = -5$

Hence,

The solution is x = -5

Keywords: Exponents, Equations

Learn more about exponential equations at:

• brainly.com/question/1993757
• brainly.com/question/2115122

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