If 3 Superscript 2 x + 1 Baseline = 3 Superscript x + 5, what is the value of x? 2 3 4 6
2 answers:
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Answer:
-2.71
Step-by-step explanation:
This exponential equation can be solved by rewriting it so there is only one base, then using logarithms.
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<h3>solve for x</h3>2^x = 3^(x+1) . . . . . given
2^x = 3·3^x . . . . . . eliminate the constant in the exponent
(2/3)^x = 3 . . . . . . . divide by 3^x
x·log(2/3) = log(3) . . . . take logarithms
x = log(3)/log(2/3) ≈ -2.7095113
The value of x is about -2.71.
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<em>Alternate solution</em>
Taking logarithms transforms this exponential equation to a linear equation.
x·log(2) = (x +1)·log(3) . . . . take logs
x(log(2) -log(3)) = log(3) . . . . . . subtract x·log(3)
x = log(3)/(log(2) -log(3)) = log(3)/log(2/3) . . . . . same result as above
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<em>Additional comment</em>
In the attached, we have used a graphing calculator to find the x-intercept of the function f(x) = 0, where f(x) = 2^x -3^(x+1). This is the solution to the given equation.
The applicable rules of logarithms are ...
log(a^b) = b·log(a)
log(a/b) = log(a) -log(b)
Answer:
The answer is
A. 529.66 ft²
Step-by-step explanation:
The picture of the composite figure is not given,
But find attached the figure.
The composite consists of two solid shapes
1. Cylinder
2. Rectangular prism
To solve for the total surface area of the composite
Let us solve for the total surface area of the cylinder
Given radius r= 4ft
Height h=5ft
A= πr²+2πrh-πr²
N/B we subtracted the second circular surface since it is joined to the rectangular prism
A= 3.142*4²+2(3.142)*4*5-3.142*4²
A= 50.272+125.68-50.272
A=125.68ft²
We proceed to find the area of the rectangular prism
We know that the prism has 6 sides
Hence area
A= 2(11*6)+ 2(8*6)+2(11*8)
A= 132+96+176
A= 404ft²
Hence total surface area is
404+125.68= 529.68ft²
