Solve each equation 1) log5-log2x=1 2) 2log(x+1)=5

Answers

Answer 1

Answer: $1)\nlog5-log2x=1;\ D:x > 0\n\nlog(5:2x)=log10\n\nlog(5)/(2x)=log10\iff(5)/(2x)=10\n\n20x=5\ \ \ /:20\n\nx=(1)/(4)\in D$

$2)\n2log(x+1)=5;\ D:x+1 > 0\to x > -1\n\nlog(x+1)^2=log10^5\iff(x+1)^2=10^5\n\nx+1=-√(10^5)\ \vee\ x+1=√(10^5)\n\nx+1=-√(10^4\cdot10)\ \vee\ x+1=√(10^4\cdot10)\n\nx=-100√(10)-1\notin D\ \vee\ x=100√(10)-1\in D$

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Karen is 6 years older than Michelle and Michelle is 2 years younger then their brother. The sum of their ages is 62 how old is michelle

Answers

Let Karen, Michelle and their brother be represented by constants k, m and b respectively.

According to your question,

k = 6 + m
b = m + 2
k + b + m = 62.

Substituting for k and b in equation 3,

(6 + m) + (m + 2) + m = 62

= 3m + 8 = 62

3m = 54
m = 18.

Thus, k = 6 + m = 24
b= m + 2 = 20.

Thus, Karen's age is 24, Michelle's age is 18 and their brother's age is 20

75 to 45 simplest form

Answers

75 : 45 = 15 : 9 (divided both number by 5 )
= 5 : 3 ( divided both numbers by 3 )

hence, 5 : 3 is the simplest form of 75 : 45
Or you can write it in the fraction form = 5 / 3

75/45 in the simplest form is 5:3, 5 to 3, or 5/3

The low temperature for 5 days was -5, -7 ,-2,2,and -3. What was the average low temperature for those days? Plz help! :)

Answers

The average means adding all the numbers and dividing by how many numbers there are.

So the average is:

$(-5 -7 -2 + 2 - 3)/(5) = (-15)/(5) = -3$

The average low was -3

Edward is playing a game where he draws cards with integers on them from a deck of cards. If the integer is positive he moves forward that many steps, if the integer is negative he moves back that many steps. Edward drew the following cards: 3, -3, -4, 5, 10, -7. Where does Edward end up in relation to where he started? A) 4 steps behind where he started. B) 4 steps in front of where he started. C) 32 steps behind where he started. D) 32 steps in front of where he started.

Answers

The correct answer is option B) 4 steps in front of where he started.

Edward moves forward 3 steps, then back 3 steps, then back 4 steps, then forward 5 steps, then forward 10 steps, and finally back 7 steps.

The total number of steps Edward moves forward is 3 + 5 + 10 = 18 steps.

The total number of steps Edward moves back is 3 + 4 + 7 = 14 steps.

So, Edward ends up 18 - 14 = 4 steps in front of where he started.

Therefore, the correct answer is option B) 4 steps in front of where he started.

To know more about an expression follow

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Nick has $8.00. Bagels cost $0.75 each, and a small container of cream cheese costs $1.25. Write an equation to represent the situation and determine the number of bagels that Nick can purchase to spend his total $8.00