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
Butoxors [25]
2 years ago
15

If logb2=x and logb3=y, evaluate the following in terms of x and y:

Mathematics
1 answer:
Alja [10]2 years ago
3 0

log_b{162} = x + 4y\\\\log_b324 = 2x+4y\\\\log_b\frac{8}{9} = 3x-2y\\\\\frac{log_b27}{log_b16} = 3y-4x

<em><u>Solution:</u></em>

Given that,

log_b2 = x\\\\log_b3 = y --------(i)

<em><u>Use the following log rules</u></em>

Rule 1: log_b(ac) = log_ba + log_bc

Rule 2: log_b\frac{a}{c} = log_ba - log_bc

Rule 3: log_ba^c = clog_ba

a) log_b{162}

Break 162 down to primes:

162 = 2^1 \times 3^4

log_b{162} =log_b 2^1. 3^4\\\\By\ rule\ 1\\\\ log_b{162} = log_b 2^1 +log_b 3^4\\\\By\ rule\ 3\\\\1log_b2 + 4log_b3\\\\1x+4y\\\\x+4y

Thus we get,

log_b162 = x + 4y

Next

b) log_b 324

Break 324 down to primes:

324 = 2^2 \times 3^4

log_b324 = log_b 2^2.3^4\\\\By\ rule\ 1\\\\log_b324 = log_b2^2 + log_b3^4\\\\By\ rule\ 3\\\\log_b324 = 2log_b2 + 4log_b3\\\\From\ (i)\\\\log_b324 = 2x + 4y

Next

c) log_b\frac{8}{9}

By rule 2

log_b\frac{8}{9} = log_b8 - log_b9\\\\log_b\frac{8}{9} = log_b 2^3 - log_b3^2\\\\By\ rule\ 3\\\\log_b\frac{8}{9} =  3 log_b2 - 2log_b3\\\\From\ (i)\\\\log_b\frac{8}{9} =  3x - 2y

Next

d) \frac{log_b27}{log_b16}

By rule 2

\frac{log_b27}{log_b16} = log_b27 - log_b16\\\\ \frac{log_b27}{log_b16} = log_b3^3 - log_b2^4\\\\By\ rule\ 2\\\\ \frac{log_b27}{log_b16} = 3log_b3 - 4log_b2 \\\\From\ (i)\\\\\frac{log_b27}{log_b16} =  3y - 4x

Thus the given are evaluated in terms of x and y

You might be interested in
9y -4y+3 if y =7 solve this
BigorU [14]
Plug 7 into each y. 9(7) -4(7) +3
63-28+3
The answer is 38
5 0
2 years ago
After last week's victory, he bought 2 medium pizzas and 1 large pizza, which is the perfect amount for the 9 players that got t
Fynjy0 [20]

Answer:

Kahoot: The Emoji Quiz

Meet: wff-qjue-fja

DONT WORRY IM NOT A OLD MAN

PLSDHQGH.

Step-by-step explanation:

8 0
3 years ago
The sum of three numbers is 108. The second number is four times greater than the first number, and the third number is 18 more
tankabanditka [31]

Answer:

450

Step-by-step explanation:

108 x 4 +18

6 0
3 years ago
Please help, I’m MARKING BRAINLIEST..
Vanyuwa [196]
If AB is parallel to CD, then A’B’ is parallel to C’D’.
5 0
3 years ago
Read 2 more answers
Graph the image of this figure after a dilation with a scale factor of 1/3 centered at the origin.
posledela

Answer:

see attached diagram

Step-by-step explanation:

A dilation with a scale factor of \dfrac{1}{3} centered at the origin has a rule:

(x,y)\mapsto\left(\dfrac{x}{3},\dfrac{y}{3}\right).

Then the image of the triangle ABC is triangle DEF(see attached diagram) with coordinates

  • D\left(\dfrac{-3}{3},\dfrac{3}{3}\right)\Rightarrow D(-1,1);
  • E\left(\dfrac{3}{3},\dfrac{9}{3}\right)\Rightarrow E(1,3);
  • F\left(\dfrac{6}{3},\dfrac{6}{3}\right)\Rightarrow F(2,2).

3 0
3 years ago
Other questions:
  • Last week,a share of stock gained a total of 1.64 points.express this gain as a mixed number in simplest form
    5·1 answer
  • What is the equivalent of 2/5 x 3/8
    10·1 answer
  • Question 1 (1 point)
    12·1 answer
  • A weather station on the top of a mountain reports that the temperature is currently 0 ∘ C and has been falling at a constant ra
    8·1 answer
  • It took Michael 279 hours to drive home because of traffic. His sister drove the same distance in 12 of Michael’s time. How long
    15·1 answer
  • Does anybody understand this?
    13·1 answer
  • Multiply:<br><br> 2 1/4 x 1 1/2 x 5/3=?
    8·1 answer
  • PLZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ HELP
    7·2 answers
  • 1. Solve the following inequality -2(x - 4) &gt; -10.<br><br><br> I need this with Work shown pls
    14·1 answer
  • Ill give brainliest hurry plssss
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!