Answer:
The solution is x = e⁶
Step-by-step explanation:
Hi there!
First, let´s write the equation
ln(x⁶) = 36
Apply logarithm property: ln(xᵃ) = a ln(x)
6 ln(x) = 36
Divide both sides of the equation by 6
ln(x) = 6
Apply e to both sides
e^(ln(x)) = e⁶
x = e⁶
The solution is x = e⁶
Let´s prove why e^(ln(x)) = x
Let´s consider this function:
y = e^(ln(x))
Apply ln to both sides of the equation
ln(y) = ln(e^(ln(x)))
Apply logarithm property: ln(xᵃ) = a ln(x)
ln(y) = ln(x) · ln(e) (ln(e) = 1)
ln(y) = ln(x)
Apply logarithm equality rule: if ln(a) = ln(b) then, a = b
y = x
Since y = e^(ln(x)), then x =e^(ln(x))
Have a nice day!
This is a simple exercise with rates.
You just have to divide the total profit of the store, that year, per the profit of the particular store.
[3.0479×10⁸ dollars] ÷ [2.102×10⁶ dollars] = 1,45 x 10²
I would but my teacher has a ad blocker on and I cant access the attachment :P
The dimension of the document is 35 inches by 40 inches.
It is redrawn at a scale of 1 1/2 or 3/2 or 1.5
The dimension will be:
35 * 1.5 = 52.5 in
40 * 1.5 = 60 in
Then redrawn again at 1/4 or 0.25
52.5 * 0.25 = 13.125 in
60 * 0.25 = 15 in
So the final dimensions of the drawing is 13.125 in by 15 in
So,
The secret to solving problems with ratios is to find the value of one unit.
5:7 = 12 units total
To find one unit, divide the total number of students by the total number of units.
600/12 = a
Simplify
50/1 = a
50 = a
The value of each unit is 50.
Now, multiply the units by the numbers in the ratio.
50(5) = b
250 = boys
50(7) = x
350 = x
There are 350 girls.
