1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Helga [31]
4 years ago
5

Solve the equation (linear equation)

%20%3D%28%5Cfrac%7B3%7D%7B4%7D%29%5E%7Bx-7%7D" id="TexFormula1" title="(\frac{16}{9}) ^{2x +5} =(\frac{3}{4})^{x-7}" alt="(\frac{16}{9}) ^{2x +5} =(\frac{3}{4})^{x-7}" align="absmiddle" class="latex-formula">
Mathematics
1 answer:
nignag [31]4 years ago
6 0

Answer: x=-\frac{3}{5}

Step-by-step explanation:

By the negative exponent rule, you have that:

(\frac{1}{a})^n=a^{-n}

By the exponents properties, you know that:

(m^n)^l=m^{(nl)}

You can rewrite 16 and 9 as following:

16=4²

9=3²

Therefore, you can rewrite the left side of the equation has following:

(\frac{4^2}{3^2})^{(2x+5)}=(\frac{3}{4})^{(x-7)}\\\\(\frac{3^2}{4^2})^{-(2x+5)}=(\frac{3}{4})^{(x-7)}\\\\(\frac{3}{4})^{-2(2x+5)}=(\frac{3}{4})^{(x-7)}

 As the base are equal, then:

-2(2x+5)=x-7

Solve for x:

-2(2x+5)=x-7\\-4x-10=x-7\\-4x-x=-7+10\\-5x=3\\x=-\frac{3}{5}

You might be interested in
Name the set or sets of numbers to which the square root of 28 belongs to.
ki77a [65]
SOLUTION: name the set or sets of numbers on a numbers to which each real number bleongs question 1) negative square root of 64 question 2) 8/3 question 3) square root 28 questio. , so it is a Real Number, Rational Number, and Integer. is a fraction, so it is a Real Number and a Rational Number.

Hope this helped! Brainliest?
8 0
3 years ago
suppose you inherited a house that was purchased in 1950 for $20,000. It is now 2015 and the value of the house has increased by
Ber [7]

Step-by-step explanation:

hope it helps

hdjsjjskkaksjs

3 0
3 years ago
HELP I WILL MARK BRAINLIEST!!!
MrMuchimi

Answer:

17.7 as the actual gas mileage recorded is 12 mpg.

Step-by-step explanation:

8 0
3 years ago
What is the solution to 2 In x = 4 In 2?
Rina8888 [55]

Answer:

= 8 in.

Step-by-step explanation:

2in× = 4in²

2in× = 16in

divide both sides by 2.

= 8 in.

7 0
3 years ago
What does the graph of lnx look like?
qwelly [4]
This is what the graph of in(x) looks like

7 0
3 years ago
Other questions:
  • Olivia ordered cupcakes and a layer cake. Together she paid $52. She paid $12 more on the layer cake than on the cupcakes. What
    7·1 answer
  • Part a :<br> part b:<br> part c :<br> part d :
    15·1 answer
  • A model rocket is launched from a roof into a large field. The path of the rocket can be modeled by the equation y=-0.06x^2+9.6x
    5·1 answer
  • Label from least to greatest 1/3, 5/6, 1/8, 7/12
    10·1 answer
  • PLEASE ANSWER QUICK! I REALLY NEED HELP!
    10·1 answer
  • (1/p-p)(1/p-q)-q/p^2(1/q+qp^2)​
    5·1 answer
  • Enter five expressions: a sum, a difference, a product, a quotient, and one that involves at least two operations that have the
    9·1 answer
  • Are the triangles similar? If so, what is the scale factor which converts RPQ to VAQ
    15·1 answer
  • For R(x) --4x+2, find f(x) when x = -1.<br> a<br> -4<br> 6<br> b<br> C<br> -2<br> d<br> 2
    7·2 answers
  • A store sold 200 cell phone covers in April. The circle graph shows the
    15·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!