Solve.
27^x+2=81

Algebra 2

x = -2/3

Step-by-step 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

x = -2/3

Step-by-step 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

step-by-step explanation:

a.   since the profit made in 2012 is equal to the profit made in 2014, the profit is           symmetric about the line y = 120,000.

step-by-step explanation:

given that megan owns a clothing boutique.

the profits of 2010, 11, are recorded and shown as follows:

years since     2010 0     1     2     3       4       5

profits made in 1000's   39       84     111     120   111     84

we find that profit gradually increases form 2010 to 2013 upto 120,   then starts decreasing.

the profits for 2012 and 2014 are the same while that of 2011 and 2015 are also the same.

this shows that there is symmetry about the line profit = 120000

hence answer is:

a.   since the profit made in 2012 is equal to the profit made in 2014, the profit is           symmetric about the line y = 120,000.

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