All categories

3 years ago

Solve this equation log3X + log3(x-6) = log3 7

Mathematics

1 answer:

ExtremeBDS [4]3 years ago

3 0

Hello!

log₃(x) + log₃(x - 6) = log₃(7) <=>

<=> log₃(x * (x - 6)) = log₃(7) <=>

<=> log₃(x² - 6x) = log₃(7) <=>

<=> x² - 6x = 7 <=>

<=> x² - 6x - 7 = 0 <=>

<=> x² + x - 7x - 7 = 0 <=>

<=> x * (x + 1) - 7 * (x + 1) = 0 <=>

<=> (x + 1) * (x - 7) = 0 <=>

<=> x + 1 = 0 and x - 7 = 0 <=>

<=> x = -1 and x = 7, x ∈ { 6; +∞ } <=>

<=> x = 7

Good luck! :)

You might be interested in

Find the value of cos E rounded to the nearest hundredth, if necessary. please help thanks

bonufazy [111]

Answer:

cos(E)=0.8

Step-by-step explanation:

cos(E)=adjacent/hypotenuse

Using a common pythagorean triple, we can find that side GE is 30 (18^2+24^2=30^2)

Then we just get cos(E)=24/30, which is 0.8

4 0

2 years ago

I’m the diagram, AB and CD are ______. A. Common external tangents B. Common internal tangents C. Uncommon tangents D. Simultane

alexgriva [62]

Answer:

It Is A

Step-by-step explanation:

3 0

3 years ago

For Spirit Day, each 8th-grade

Mrac [35]

Answer: Option A

P(B and V)=10%

Step-by-step explanation:

To solve this poroblema we use the formula of combinations:

$nCr =\frac{n!}{r!(n-r)!}$

Where n is the number of objects that can be chosen and you choose r from them.

There are 5 colors of shirts.

The number of shirts that can be made by combining 2 of the 5 possible colors is calculated as:

$5C2$

$5C2=\frac{5!}{2!(5-2)!}$

$5C2=10$

The number of shirts that can be made by combining 2 of the 2 possible colors (B) and (V) is calculated as:

$2C2 = 1$

Then the probability is:

$P(B\ and\ V)=\frac{2C2}{5C2}\\\\P(B\ and\ V)=\frac{1}{10}\\\\P(B\ and\ V)=0.1=10\%$

6 0

4 years ago

Read 2 more answers

Kevin is observing the population of the fish he put into a pond. He built a pond and populated it with 500 fish. The population

laila [671]

Here we will use exponential form, which is

$y = y_{0} e^{kt}$

Initial value, y0 = 500

Double of 500 = 1000

$1000 = 500e^{k*1}$

$2 = e^k$

$k= ln (2)$

Required equation is

$y=500e^{x ln2} \\ y= 500 (2)^x$

6 0

4 years ago

The expression p/x^2 - 5x +6 simplifies to x+4/x-2. Which expression doees p represent?

gladu [14]

We know that
(ad)/(bd)=d/d time a/b=a/b since d's cancel
also
if a/b=c/d in simplest form, then a=c and b=d

we have
p/(x^2-5x+6)=(x+4)/(x-2)
therefor

p/(x^2-5x+6)=d/d times (x+4)/(x-2)
p/(x^2-5x+6)=d(x+4)/d(x-2)

therefor
p=d(x+4) and
x^2-5x+6=d(x-2)

we can solve last one
factor
(x-6)(x+1)=d(x-2)
divide both sides by (x-2)
[(x-6)(x+1)]/(x-2)=d
sub

p=d(x+4)
p=([(x-6)(x+1)]/(x-2))(x+4)
$p= \frac {(x-6)(x+1)(x+4)}{(x-2)}$

7 0

3 years ago