Solve for x

1. log(x+9)=log(2x-7)

2. log(x-1)^2=log(-5x-1)

Lets first solve the first one:

log(x+9)=log(2x−7)

Convert the logarithmic equation to an exponential equation.

10^log(x+9)=10^log(2x−7)

Remember that 10^logx=x, so

x+9=2x−7

Move values with 'x' to the right hand side.

7+9=2x-x

Combine like terms.

16=x so,

x=16

Check:

log(x+9)=log(2x−7)

If x=16

log(16+9)=log(2(16)−7)

log25=log(32−7)

log25=log25

x=16 is a solution.

Solve the second one like i solved this one, try it

connie < felicia < stew

step-by-step explanation:

stew:

we need to find the slope

m = (y2-y1)/ (x2-x1)

    = (2650-795)/(10-3)

    = 1855/7

265 words per minute

connie:

we need to find the slope

m = (y2-y1)/ (x2-x1)

we have two points (0,0) and (4,800)

m = (800-0)/(4-0)

  m = 800/4

    200 words per minute

felicia:

260 words per minute

200< 260 < 265

connie < felicia < stew

question: how many people can she serve?

answer: she can serve 16.66666667 people. so she can only give 16 people a complete serving.

question: does she have enough ice cream for her guests?

answer: no. explanation: she only has enough for 16 people to have a full serving. however, she can give a 17th person a partial serving.