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mihalych1998 [28]
3 years ago
12

What is the solution to the equation 9^(x+1) =27

Mathematics
2 answers:
azamat3 years ago
6 0

ANSWER

x =  \frac{1}{2}

EXPLANATION

The given exponential equation is

{9}^{x + 1}  = 27

The greatest common factor of 9 and 27 is 3.

We rewrite the each side of the equation to base 3.

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

Since the bases are equal, we can equate the exponents.

2(x + 1) = 3

Expand the parenthesis to get:

2x + 2 = 3

Group similar terms

2x = 3 - 2

2x = 1

x =  \frac{1}{2}

Kazeer [188]3 years ago
6 0

For this case we must solve the following equation:

9 ^ {x + 1} = 27

We rewrite:

9 = 3 * 3 = 3 ^ 2\\27 = 3 * 3 * 3 = 3 ^ 3

Then the expression is:

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

Since the bases are the same, the two expressions are only equal if the exponents are also equal. So, we have:

2 (x + 1) = 3

We apply distributive property to the terms within parentheses:

2x + 2 = 3

Subtracting 2 on both sides of the equation:

2x = 3-2\\2x = 1

Dividing between 2 on both sides of the equation:

x = \frac {1} {2}

Answer:

x = \frac {1} {2}

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