Question

Solve.
27^x+2=81

Algebra 2

Answer 1

x = -2/3

Explanation:

We'll employ our knowledge of indices and exponential resolution to solve the problem.

First, we'll make efforts to resolve this figures such that the bases will be of thesame figure.

Our priority will be on "27" and "81"

27= 3*3*3

27 = 3^3

81 = 3*3*3*3

81 = 3^4

Therefore, let's solve now!

27^(x + 2) = 81

3^3 (x + 2) = 3^4

We'll then use the exponent 3 to expand the bracket that is 3(x+2)

3 ^ (3x + 6) = 3^4

The bases in 3 will cancel out! The equation becomes:

3x + 6 = 4

3x = 4 - 6

3x = -2

x = -2/3

Math is fun

Answer 2

x = -2/3

Explanation:

27 ^(x+2) = 81

Rewrite 27 as a power of 3

27 = 3^3

Rewrite 81 as a power of 3

3^4

3^3^(x+2) = 3^4

We know that a^b^c = a^(b*c)

3^3*(x+2) = 3^4

3^(3x+6) = 3^4

The bases are the same so the exponents are the same

3x+6 = 4

Subtract

6 from each side

3x+6-6 =4-6

3x = -2

Divide by 3

3x/3 =-2/3

x = -2/3