3 to the power 2x+3 is subtracted by 9 which is equal to 2 times 9 to the power x+1 and is subtrcted by 6

Answer:

x = -0.5

Step-by-step explanation:

Here we have the sentence:

"3 to the power 2x+3 is subtracted by 9 which is equal to 2 times 9 to the power x+1 and is subtracted by 6"

The first part:

"3 to the power 2x+3 is subtracted by 9..."

This can be written as:

[tex]3^{2x + 3} - 9[/tex]

"... is equal to 2 times 9 to the power x+1 and is subtracted by 6"

[tex]3^{2x + 3} - 9 = 2*9^{x + 1} - 6[/tex]

Let's solve this for x.

First, we can add 9 in both sides:

[tex]3^{2x + 3} = 2*9^{x + 1} - 6 + 9 = 2*9^{x + 1} + 3[/tex]

We also know the relations:

[tex]a^n*a^b = a^{n + b}[/tex]

and

[tex](a^n)^m = a^{n*m}[/tex]

We can write the left part as:

[tex]3^{2x + 3} = 3^{2x}*3^3 = (3^2)^x*3^3 = 9^x*27[/tex]

And the right side as:

[tex]2*9^{x + 1} + 3 = 2*9^x*9 + 3 = 18*9^x + 3[/tex]

Then the equation becomes:

[tex]27*9^x = 18*9^x + 3[/tex]

Now let's move both terms with 9^x to the left side:

[tex]27*9^x - 18*9^x = 3\\[/tex]

[tex](27 - 18)*9^x = 3[/tex]

[tex]9*9^x = 3[/tex]

[tex]9^x = 3/9 = 1/3[/tex]

Now remember that:

Ln(a^b) = b*Ln(a)

Then if we apply the Ln( ) function to both sides, we get:

[tex]Ln(9^x) = Ln(1/3)[/tex]

[tex]x*Ln(9) = Ln(1/3)[/tex]

[tex]x = \frac{Ln(1/3)}{Ln(9)} = -0.5[/tex]

How much will it cost to paint the treasure chest below? A pint of paint can cover 5 ft2 and costs $4.50. You do not need to paint the bottom of the treasure chest.
please show work. its late for geometry and I really need to pass. i will mark brainliest :)

let me know if this is 160 sheeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeesh this food bussin bussin

During summer, when the snow melts, the water level of the Yukon River increases. If the water level of the river increased by 54 centimeters in 6 days, what is the water level increase rate in centimeters per day

For the past week, your restaurant revenue was $28,675 and your food cost was $9,274. Calculate your gråss margi

percentage (revenue - food cost)lrevenue). Remember to round to the nearest percent.

a) 63%

b) 68%

C) 73%

d) 78%

Find the distance between the points (1,8) and (9, 2).
Write your answer as a whole number or a fully simplified radical expression. Do not round.
units

what is the gcf of 150 and 3

What are two step equations that equal 17?

pls show the process

Evaluate the expression below when x = 4, y = 5

3(y-x) + 4y

What is the value of the expression?
5 (3+4)
A 19
B) 35
C 12
D) 60

| Juan wants to put carpeting in his living
room. The room is 15ft. by 13 ft. The
carpeting will cost $16.99 per square foot.
What is the cost of the carpeting? 2 steps
a) $195.00
b) $3,313.05
c) $2548.50
d) $3,300.00

Can anyone help me I need to find the area, please help

a square tile has width of 1/4 foot. how many tiles will fit end to end along a 4 foot wall
16 tiles
8 tiles
4 tiles
1 tile​

fill in the blank 3(2+7a)=6+

Data collected for 300 fish for north atlantic. The length of the fish (in cm) is summarized in the histogram below.

state whether 0 is a rational number​

Help me with this please

Write the powerset of the following sets
a) {3,7,9}
b) {a,{ 1,2}}
c) {p,q,r,s}
​

Dave made two boxes. The sides of the second box are each of the sides of the first box How are the volumes of the two boxes related?​

PLS ANYONE HELP ASAP!!!!

[tex] \sqrt{9 {}^{4} } [/tex]
​

The scatter plot suggests a relationship between time and the distance from the destination. The equation of the line of best fit is y=-0.6x+15, and the correlation coefficient is -0.8. Which best describes the correlation between the two variables?

a. weak positive
b. strong positive
c. weak negative
d. strong negative

Answer the statistical measures and create a box and whiskers plot for the following set of data.
2, 4, 4, 6, 6, 6, 7, 9, 10, 13, 13, 13, 15



Min:

Q1:

Med:

Q3:

Max:

I will give brainliest if you get this right

Can someone pls help me with: Ooh
Okay
(Baby Ruth, Baby Ruth)
They always say "Ooh, Baby Ruth" (haha)
How you get your eyes so baby blue? (Blue, blue)
(Get it, bro)
"All he does is clout chase" (mm-hmm)
Yeah, b!ch, it's my mf name (uh-oh)
News flash, you'll never be me (uh-huh)
Me and Claire are like Mike (yup)
Pippen (yup), 3 PEAT
Venmo me
Venmo me
Venmo me
B!ch, I said "Venmo me, Venmo me" (Venmo me)
I'm livin' in your head rent free, b!ch
Fug Noah Miller, tryna be me (get it sis)
I-I-I'm just a kid, b!ch, I'm only 15 (hey)
I said "Best friend, put me on that beat" (okay)
Now I'm here, put that chorus on repeat
Venmo me
Venmo me
Venmo me
If you say so then I'ma dance
Every time I throw it back, I take all you b!ches' mans (ahh)
I'ma pull up to the Hype House and Tony can catch these hands (hit that b!ch)
Did a little dance under the money tree
Don't forget the dance creds: yodelinghaley
That Yodel Girl, yeah, you know
Spittin' heat, need aloe
All you b!ches is slow and talking shii on the low
Body roll then I woah
Jahluver is emo
You got a problem with me? Then why don't you say so?
Okay, I don't know if you needed any of that
This was really embarrassing
Please never show...
Hey, guys, you forgot to invite me, again
Why didn't you guys invite me? Omg
You don't know what you just did
You could hurt... You decided... Find me...
Oh my god, you're gonna recruit...
You-you don't know what
You-you-you don't know f... ??

Consider the geometric sequence 8,4,2,1,...

A number c is more than 20 inequality PLEASE HELP NOW IT EASY

what is the cube root of 8​

What is the solution to the inequality? 2x-5<17

Brainliest!!!!!marking<—