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]
3 years ago
15

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

Mathematics
1 answer:
Alja [10]3 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
Fine slope intercept form <br> y = x+7 (2, 3)<br> Help please and thanks
Dimas [21]

Answer:

y=x7 X 5

Step-by-step explanation:

6 0
3 years ago
Ricardo has agreed to tutor for the school. He owes his older brother $59 and would like to end the summer with at least $400 in
Dvinal [7]

Answer:

44 or 45

Step-by-step explanation:

400 divided by nine

5 0
2 years ago
Read 2 more answers
There are 8 roses in a vase of 13 flowers. The rest are daisies.
Blizzard [7]

Answer:

  1. 5:13
  2. 8:5

Step-by-step explanation:

For first part:

  1. Roses = 8
  2. Daises = All flowers - Roses
  3. Daises = 13 - 8
  4. Daises = 5
  5. Daises:All Flowers = 5:13

For second part:

  1. Roses:Daises = 8:5

I hope this helps!

7 0
3 years ago
Read 2 more answers
This is an accounting question: On September 23, Reese Company received a $350 check from Mike Moluf for services to be performe
svlad2 [7]

Not to seem rude, but you might have better luck in Business. Unless someone here know accounting lol

3 0
3 years ago
Three minus the quotient of a number x and 12
attashe74 [19]

Answer:

3 - x/12

Step-by-step explanation:

follow the steps in the sentence

7 0
3 years ago
Other questions:
  • In ΔMNO, the measure of ∠O=90°, the measure of ∠N=70°, and OM = 3.3 feet. Find the length of MN to the nearest tenth of a foot.
    11·1 answer
  • Find the proportion of the missing number 7/a = 2/4
    5·1 answer
  • Which linear equation has no solution? 23(9x+6)=6x+4
    6·1 answer
  • A farmer can buy two types of plant​ food, mix A and mix B. Each cubic yard of mix A contains 35 pounds of phosphoric​ acid, 15
    8·1 answer
  • Write the number 100 as a product of its prime factors in the same way.
    12·1 answer
  • MODELING A WATER WHEEL
    11·2 answers
  • Jason invests money in an account paying simple interest. He invests $160 and no money is added or removed from the investment.
    12·2 answers
  • A triangle has a base of 15 and an area of 165. What is the height of the triangle?
    6·2 answers
  • -2 &lt; n &lt;_ 6<br><br> n is an integer. What is the possible values of n?
    13·1 answer
  • The population of Bloom Falls, Mass (population 937)is slowly moving to a
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!