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

Question

asked Jul 13, 2020 175k views

2 Answers

Michael Gattuso · Answer 1 · 2020-07-13T22:51:53+0000

ANSWER

x = (1)/(2)

Step-by-step 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 = (1)/(2)

Latrunculia · Answer 2 · 2020-07-17T23:24:34+0000

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:

$x = \frac {1} {2}$