Which 2 options are correct?
1 answer:
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Answer:
The equivalent statement is ⇒ 2nd answer
Step-by-step explanation:
* Lets explain how to solve the problem
- Any root can be a fraction power
- Ex:
* The expression is
∵ can be written as
∵
∴ =
* The equivalent statement is
Answer:
Given the function: .....[1]
An exponential function is in the form of .
- If
and b <1, then the graph is increasing
- If a< 0 and b >1 , then the graph is decreasing.
- If a> 0 and b<1, the the graph is decreasing.
- if a< 0 and b > 1. then the graph is increasing.
From the given equation [1] we have;
Here, a = -2 < 0 and b = 3 > 1.
For this function, x-intercepts doesn't exist, as it does not crosses the x-axis graph.
y-intercept states that the graph crosses the y-axis.
Substitute value of x =0 in [1] to solve for y;
y = -2
y-intercept = (0, -2)
End Behavior of the given graph :
If , then
and
If , then
Also, You can see the graph as shown below in the attachment.
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)
