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
Mekhanik [1.2K]
3 years ago
12

If log 2 = x and log 3 = y, write each logarithm in terms of x and y.

Mathematics
1 answer:
Korvikt [17]3 years ago
8 0

Answer:

  • a) x+y
  • b) 2x+y
  • c) -x
  • d) x+y+1
  • e) y-x
  • f) x/2

Step-by-step explanation:

The applicable rules of logarithms are ...

  log(ab) = log(a) +log(b)

  log(a^b) = b·log(a)

__

\text{a)  }\log{6}=\log{(2\cdot 3)}=\log{2}+\log{{3}=\boxed{x+y}

\text{b)  }\log{12}=\log{(2^23)}=2\log{2}+\log{3}=\boxed{2x+y}

\text{c)  }\log{(1/2)}=\log{2^{-1}}=-\log{2}=\boxed{-x}

\text{d)  }\log{60}=\log{(2\cdot 3\cdot 10)}=\log{2}+\log{3}+\log{10}=\boxed{x+y+1}

\text{e)  }\log{1.5}=\log{3\cdot2^{-1}}=\log{3}-\log{2}=\boxed{y-x}

\text{f)  }\log{\sqrt{2}}=\log{2^{\frac{1}{2}}}=\dfrac{1}{2}\log{2}=\boxed{\dfrac{x}{2}}

You might be interested in
Can someone help me with only #17, B?
Oxana [17]

Answer:

2.5x

Step-by-step explanation:

6 0
3 years ago
5k race surveyed runners about their finishing times (f) and the number of previous races they had run (n). The organizers found
vichka [17]
I FOUND YOUR COMPLETE QUESTION IN OTHER SOURCES.
 
SEE ATTACHED IMAGE, PLEASE.
 
The first thing we must do for this case is to define variables.
 n = number of 5k races covered
 f = end time.
 We have the following equation:
 f = -1.2n + 38.1
 We note that the slope of the line is:
 m = -1.2 minutes per race
 Therefore, the time decreases 1.2 minutes when the number of races increases n.
 Answer:
 
The model predicts that for each additional race to runner has run, the finishing time decreases by about 1.2 minutes

3 0
3 years ago
Name the value of the 5's in the number 5,500
alisha [4.7K]
First 5 : five thousand
second 5 : five hundred
5 0
4 years ago
Louis is very hungry when he spots a hot dog stand. The stand sells soft drinks for $1.25 each and hot dogs for $2.50 each. Loui
pshichka [43]

Answer:

7 hot dogs

Step-by-step explanation:

Set up an equation:

2.5x + 1.25 = 21

2.5x = 19.75

x = 7.9

You cannot buy .9 of a hot dog, so the answer is 7

7 0
2 years ago
BRAINLIEST ASAP! PLEASE HELP ME :)
nikdorinn [45]

Answer:

m <1 = 61

Step-by-step explanation:

We know that the angle adjacent to 130 is 50 degrees because linear angles are complementary.

Extending line t to make a triangle, we can find the angle adjacent to the angle labeled 111  ( and above it) is 69.

That makes the angle that touches line q 61 to finish the triangle

This angle and angle 1 are corresponding angles, so they are equal

<1 = 61

7 0
3 years ago
Other questions:
  • Solve 3/x^2-8=2<br> Help pleaseeeee
    7·1 answer
  • The sum of two consecutive even intergers divided by four is 189.5
    7·2 answers
  • What is the tangent ratio for
    8·1 answer
  • Holly is trying to save $25,000
    10·2 answers
  • Having been heard of by the local townspeople for your successful mission for King Domke, you have been approached by the local
    7·1 answer
  • ❗️5 points❗️<br> state the slope of the line.<br> A. -2<br> B. 0<br> C. 1<br> D. undefined
    5·1 answer
  • 48 divided by 6 equals 16 -n
    7·2 answers
  • Lines A and B are parallel and are intersected by line C. Given angle 1 is 145°, what is the sum of the measures of angles 1, 2,
    7·1 answer
  • Carla paid $129 plus 6% sales tax for a guitar. What
    11·1 answer
  • The whole cake is 9 cm high and 20 cm across. Each layer of cake is 2cm thick, and each layer is separated by 1 cm of frosting.
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!