9514 1404 393
Answer:
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
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<em>Additional comment</em>
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.
9514 1404 393
Answer:
45
Step-by-step explanation:
The equation is that of a parabola in vertex form.
y = a(x -h)^2 +k
where 'a' is the vertical scale factor and (h, k) is the vertex.
Comparing this to the given function, you find ...
a = -5
h = 1
k = 45
The negative value of 'a' tells you the parabola opens downward, so the y-value of the vertex is the maximum value of the function: 45.
