Log3x-log3 (x − 8) = 2?

Answers

Answer 1

Answer:

Answer: To solve the equation log3x - log3(x - 8) = 2, we can use the properties of logarithms to simplify and solve for x.

First, let's apply the quotient rule of logarithms. The quotient rule states that log(base a)(b) - log(base a)(c) = log(base a)(b/c).

Using this rule, we can rewrite the equation as log3(x / (x - 8)) = 2.

Next, let's rewrite 2 as a logarithm. The logarithmic form of 2 is log(base a)(b) = c, where a^c = b. In this case, a^c = 3^2 = 9. Therefore, we can rewrite the equation as log3(x / (x - 8)) = log3(9).

Now that the bases are the same, we can set the arguments of the logarithms equal to each other. Therefore, x / (x - 8) = 9.

To solve for x, we can multiply both sides of the equation by (x - 8) to eliminate the fraction. This gives us x = 9(x - 8).

Expanding the right side of the equation, we get x = 9x - 72.

Next, we can subtract 9x from both sides of the equation to isolate x. This gives us -8x = -72.

Dividing both sides of the equation by -8, we find that x = 9.

Therefore, the solution to the equation log3x - log3(x - 8) = 2 is x = 9.

Step-by-step explanation:

Related Questions

How many seconds in an hour
State a conclusion that seems reasonable. You eat a new kind of fruit and suffer from hives for the first time in your life. A week later, you try the fruit and the hives recur. A month later, you have a similar experience. Conclusion: ?...
Find the interval on which the curve of y equals the integral from 0 to x of 2 divided by the quantity 1 plus 3 times t plus t squared, dt is concave up.
f the sample size n=25, the sample mean = 10 and the sample standard deviation s=6, create the 90% confidence interval for the population mean and interpret it. A. The confidence interval is [7.52 ,12.48] and 90% of the population values fall in this interval. B. The confidence interval is [7.52 ,12.48] and there is a 90% chance that the population mean has a value that falls within this interval. C.The confidence interval is [7.95 ,12.05] and there is a 90% chance that the population mean has a value that falls within this interval. D. The confidence interval is [7.95 ,12.05] and 90% of the population values lie within this interval.
What is the y intercept of 2x - y = -1

Can somebody please help me ASAP? It’s due today!! I will give brainliest if it’s correct Show work please

Answers

Answer: It is O 2.

Step-by-step explanation: 1. Start with the expression (7¹q5)-² (r-5s)².

2. According to the exponent rule, when we have an exponent raised to another exponent, we multiply the exponents. Therefore, we have (7¹q5)² and (r-5s)².

3. Simplifying (7¹q5)², we multiply the exponents: 7²q10.

4. Similarly, simplifying (r-5s)², we multiply the exponents: r²-10rs+25s².

5. Now, we multiply the two simplified expressions: (7²q10) * (r²-10rs+25s²).

6. Finally, we simplify the expression. The exponent of r when the expression is simplified is 2.

Therefore, the correct answer is O 2.

Elvia is job shadowing for an internship. She is required to complete at least 48 hours of shadowing in her chosen career. Elvia can shadow for 2 hours on weekdays and 6 hours on weekends. Which graph represents the number of weekdays and weekends that Elvia can shadow to meet her requirements? A.) Picture 1
B.) Picture 2
C.) Picture 3
D.) Picture 4

Answers

The graph that represents the number of weekdays and weekends that Elvia can shadow to meet her requirements is A. Picture 1

How to graph the requirements ?

To graph this inequality, we would typically draw the line representing the equation 2x + 6y = 48 and then shade the region that satisfies the inequality $2x + 6y \geq 48$ .

Since Elvia is required to complete "at least" 48 hours, the line on the graph will be solid, not dotted, to indicate that the hours represented by the line are included in the solutions that meet the requirements.

The point the graph would cross the x - axis is:

2 x + 6 ( 0 ) ≥ 48

x = 48 / 2

x = 24

The point the graph would cross the y - axis is:

2 ( 0 ) + 6 y ≥ 48

y = 48 / 6

y = 8

The correct graph is therefore Picture 1 which has the line as solid and the intercepts as x = 24 and y = 8 .

Find out more on graphs at brainly.com/question/33161009

#SPJ2

The Answer is A.)

A picture of my answer

The expression 8 x plus 12 y represents the sum of Harry and Mike’s total monthly wages, where x represents the number of hours Harry worked and y represents the number of hours Mike worked. What is another way to write the expression, and what can you conclude from rewriting it in this way?A. 8 left parenthesis x plus 1.5 y right parenthesis ; Harry’s hourly wage is 1.5 times Mike’s.
B. 8 left parenthesis x plus 1.5 y right parenthesis; Mike’s hourly wage is 1.5 times Harry’s.
C. 12 left parenthesis 8 x plus y right parenthesis ; Harry’s hourly wage is 8 times Mike’s.
D. 8 left parenthesis x plus 4 y right parenthesis ; Mike’s hourly wage is 4 times Harry’s.

Answers

it’s B figured it out got it

PLEASE HELP. A playground is shaped like a rectangle with a width 5 times its length (l). What is a simplified expression for the distance between opposite corners of the playground?

Answers

Look at the picture.

Use the Pythagorean Teorem:
$l^2+(5l)^2=d^2\nl^2+5^2l^2=d^2\nd^2=l^2+25l^2\nd^2=26l^2\nd=√(26)^2\nd=√(26)\cdot√(l^2)\n\boxed{d=l√(26)}$

I need an answer to this "How many tickles does it take to make an octopus laugh

Answers

Answer:

it takes ten tickles for an octopus to laugh

Which of the following expressions shows the expression 1/2x+3−2/5x+1 in simplest form?

Answers

Hey there!

1/2x + 3 - 2/5x + 1

COMBINE the LIKE TERMS

= (1/2x - 2/5x) + (3 + 1)

1/2x - 2/5x = 1/10x

3 + 1 = 4

= 1/10x + 4

Therefore, your answer is: 1/10x + 4

Good luck on your assignment and enjoy your day!

~Amphitrite1040:)

Answer:

$\huge\boxed{(1)/(2)x+3-(2)/(5)x+1=(1)/(10)x+4}$

Step-by-step explanation:

$(1)/(2)x+3-(2)/(5)x+1\n\n=\left((1)/(2)x-(2)/(5)x\right)+(3+1)\n\n=\left((1\cdot5)/(2\cdot5)x-(2\cdot2)/(5\cdot2)x\right)+4\n\n=\left((5)/(10)x-(4)/(10)x\right)+4\n\n=(1)/(10)x+4$

Other Questions

A line intersects the points (3,-4) and (1,2).What is the slope intercept equation for this line

Using a directrix of y = 2 and a focus of (3, −4), what quadratic function is created?

12 diminished by 6 times a number( which one is correct)1. 12-6n 2. 6n-123. 12n-6

I’m in ninth grade and don’t understand this algebra 1 question -5(3a+b)+(2a-7b)