Which of the following is the solution to the equation 3^X+9=81^X a) x=-6
b)x=6
c)x=-3
d)x=3

9514 1404 393

  d)  x = 3

Step-by-step explanation:

The given equation resolves to a quartic equation in (3^x). It has a solution near ...

  x = 0.541770946714

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Perhaps you want the solution to ...

  3^(x+9) = 81^(x)

Rewriting in powers of 3, this is ...

  3^(x+9) = (3^4)^x = 3^(4x)

Taking logarithms base 3 gives ...

  x +9 = 4x

  9 = 3x . . . . . . subtract x

  3 = x . . . . . . . divide by 3 . . . . matches choice D

Additional comment

The Order of Operations requires that exponential terms be evaluated before addition and subtraction. That means (3^x) must be evaluated before the sum (3^x) + 9. If you want the sum of x and 9 to be evaluated first, it must be in parentheses: 3^(x+9).

In typeset equations, the superscript font serves to group parts of the exponent. In plain text, a grouping symbol (parentheses) must be used.

(2,20) means that the 2 is 2 hours and 20 is 20$. so there both 20$ for 2 hours only the same price. like it says. so, the dunk tank and the bounce house are the same price (20$) for the same amount of time (2 hours).

hope i

b

step-by-step explanation: