Solve for x.
ln(x+3) = ln10 - ln(x)

x =2

Step-by-step explanation:

Solve for x:

log(x + 3) = log(10) - log(x)

Hint: | Move everything to the left hand side.

Subtract log(10) - log(x) from both sides:

-log(10) + log(x) + log(x + 3) = 0

Hint: | Combine logarithms.

-log(10) + log(x) + log(x + 3) = log(1/10) + log(x) + log(x + 3) = log(1/10 x (x + 3)):

log(1/10 x (x + 3)) = 0

Hint: | Eliminate the logarithm from the left hand side.

Cancel logarithms by taking exp of both sides:

1/10 x (x + 3) = 1

Hint: | Multiply both sides by a constant to simplify the equation.

Multiply both sides by 10:

x (x + 3) = 10

Hint: | Write the quadratic polynomial on the left hand side in standard form.

Expand out terms of the left hand side:

x^2 + 3 x = 10

Hint: | Take one half of the coefficient of x and square it, then add it to both sides.

Add 9/4 to both sides:

x^2 + 3 x + 9/4 = 49/4

Hint: | Factor the left hand side.

Write the left hand side as a square:

(x + 3/2)^2 = 49/4

Hint: | Eliminate the exponent on the left hand side.

Take the square root of both sides:

x + 3/2 = 7/2 or x + 3/2 = -7/2

Hint: | Look at the first equation: Solve for x.

Subtract 3/2 from both sides:

x = 2 or x + 3/2 = -7/2

Hint: | Look at the second equation: Solve for x.

Subtract 3/2 from both sides:

x = 2 or x = -5

Hint: | Now test that these solutions are correct by substituting into the original equation.

Check the solution x = -5.

log(x + 3) ⇒ log(3 - 5) = i π + log(2) ≈ 0.693147 + 3.14159 i

log(10) - log(x) ⇒ log(10) - log(-5) = -i π + log(2) ≈ 0.693147 - 3.14159 i:

So this solution is incorrect

Hint: | Check the solution x = 2.

log(x + 3) ⇒ log(3 + 2) = log(5) ≈ 1.60944

log(10) - log(x) ⇒ log(10) - log(2) = log(5) ≈ 1.60944:

So this solution is correct

Hint: | Gather any correct solutions.

The solution is:

x = 2

a. turk and mcalister

b. howard, mission, and market

c. yes. since streets end some do not cross yet are not parallel to others. example: mcalister and 5th

step-by-step explanation:

parallel lines are lines which do not intersect ever and look a lot like railroad tracks. turk, mcalister and golden gate are examples of these.

intersect are streets which cross each other and a car on one can reach the other. howard, mission, and market intersect with 6th.

skew lines are lines which neither intersect nor are parallel. these lines exist here because some streets end and never intersect another like mcalister and 5th.

part a

x     y

0     8

1     7.5

2     7

3     6.5

4     6

5     5.5  

for every hour i deducted .5 inches from the length of the candle

part b

it is a function because for every x value there is only one y value

part   c

for every x value there is only one y value

x       y

0       8

1       7.6

2       7.2

3       6.8

step-by-step explanation: