Which graph would help solve the equation5log(x+3)=5?
1 answer:
Method 1:
By graphing, we can find the graph of y = 5log(x + 3) and y = 5 to see where they intersect.
Method 2:
Alternatively, by subtracting 5 from both sides, we can find where the graph 5log(x + 3) - 5 hits the x-axis. In essence, we are finding when y hits 0 and thus, finding where it hits the x-axis.
Method 3:
We can also just solve this algebraically. When we don't have any superscripts, we take the assumption that we're working in base 10.
Divide both sides by 5:
Take the inverse of log(x + 3) to both sides:
Hence, we know that at x = 7, 5log(7 + 3) = 5.
The graphs of Method 1 is pictured first, and the graph of Method 2 is pictured on the right.
By graphing, we can find the graph of y = 5log(x + 3) and y = 5 to see where they intersect.
Method 2:
Alternatively, by subtracting 5 from both sides, we can find where the graph 5log(x + 3) - 5 hits the x-axis. In essence, we are finding when y hits 0 and thus, finding where it hits the x-axis.
Method 3:
We can also just solve this algebraically. When we don't have any superscripts, we take the assumption that we're working in base 10.
Divide both sides by 5:
Take the inverse of log(x + 3) to both sides:
Hence, we know that at x = 7, 5log(7 + 3) = 5.
The graphs of Method 1 is pictured first, and the graph of Method 2 is pictured on the right.
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Answer:
The 98% confidence interval for the mean purchases of all customers is ($37.40, $61.74).
Step-by-step explanation:
We have that to find our level, that is the subtraction of 1 by the confidence interval divided by 2. So:
Now, we have to find z in the Ztable as such z has a pvalue of .
So it is z with a pvalue of , so
Now, find M as such
In which is the standard deviation of the population and n is the size of the sample.
The lower end of the interval is the mean subtracted by M. So it is 49.57 - 12.17 = $37.40.
The upper end of the interval is the mean added to M. So it is 49.57 + 12.17 = $61.74.
The 98% confidence interval for the mean purchases of all customers is ($37.40, $61.74).