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
Oliga [24]
3 years ago
12

Verify each of the following by evaluating the logarithms. log10(103) + log10(104) = log10(107)

Mathematics
1 answer:
ioda3 years ago
7 0

Answer:

log₁₀(10³) + log₁₀(10⁴)

= log₁₀( 10³ × 10⁴ )

= log₁₀( 10³⁺⁴)

= log₁₀( 10⁷)

Step-by-step explanation:

Given:

log₁₀(10³) + log₁₀(10⁴) = log₁₀(10⁷)

Now,

we know the property of log function that

log(A) + log(B) = log(AB)

therefore,

applying the above property on the LHS, we get

log₁₀(10³) + log₁₀(10⁴) = log₁₀( 10³ × 10⁴ )

also,

xᵃ + xᵇ = xᵃ⁺ᵇ

therefore,

log₁₀( 10³ × 10⁴ ) = log₁₀( 10³⁺⁴)

= log₁₀( 10⁷)

Hence,

LHS = RHS

Hence proved

You might be interested in
If f(x) = -4x^2 - 5x + 2, what is f(3) ?
svp [43]
The value should be -49. Hope this helps.
5 0
2 years ago
A spinner is divided into many different color sectors. Some sectors are larger than others. The spinner was spun 300 times. The
Furkat [3]
Solutions 

We know that <span>a spinner was divided into many different color sectors. Some sectors are larger than others. The spinner was spun 300 times. The results were tallied up and were written in a table. 

</span><span>Red:93

Blue:59

Green:105

Yellow:43
</span>
The spinner landed the highest on green. To find <span>the probability that the next spin will land on green we have add all the numbers and simplify them.  

93 + 59 + 105 + 43 = 300 

Out of 300 the spinner landed to green 105 times. We have the fraction 105/300. 

105/300 can be reduced. To reduce the fraction we need to the GCF of 105 and 300. The GCF is 15. 

</span>We can reduce the fraction by dividing the numerator and denominator by the GCF = 15. 

105 ÷ 15 = 7 

300 ÷ 15 = 20 

Our new fraction is 7/20 

The <span>probability that the next spin will land on green is 7/20. 
</span>≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡
<span>
To get the answer to part (B) we have to add the results of red and green then simplify. 

93 + 105 = 198 

The fraction is 198/300. </span><span>198/300 can be reduced. To reduce the fraction we need to the GCF of 105 and 300. The GCF is 6. 

</span>We can reduce the fraction by dividing <span>the numerator and denominator by the GCF = 6.

</span>198 ÷ 6 = 33

300 ÷ 6 = 50<span>

The new fraction is 33/50 

</span>The probability that the next spin will land on either green or red is <span>33/50. 
</span>
Hope this helps 
4 0
3 years ago
What is the estimate
grigory [225]
To find the biggest or close number say 70 is close to 75 or 70 the answer would be 70 I think but not sure
3 0
3 years ago
Read 2 more answers
Ron and Ben had a total of 700 playing cards. After Ron gave away 40% of his playing cards and Ben gave away 20% of his playing
allsm [11]
Ron had 140 picture cards more than Ben
5 0
3 years ago
BRAINLIEST + 45 POINTSSSS I RLLY NEED HELPPPPPPP! PLS ANSWERRRR PROPERLY AND I WILL GVE U BOTH OF THOSE THINGS BUT I NEED IT ASA
xxMikexx [17]
Graph A because a graph of non proportional relationship will not pass through the origin (0,0) hope this helps! Remember to give me a like if it did please and thank you!
6 0
3 years ago
Other questions:
  • Your family of four has a 6 GB data limit each month. You use twice as much data as your sister, half as much data as your fathe
    15·1 answer
  • Patrick is buying a new pair of shoes. The expression shown below represents the sales tax on the price of the shoes,s. 0.06s By
    9·2 answers
  • If c(x) = 4x – 2 and d(x) = x2 + 5x, what is (cd)(x)?
    11·1 answer
  • Calculate the kinetic energy of a 0.5 kg soccer ball that is falling at a velocity of 3m/s.
    6·2 answers
  • If the original price is $40 and the discounted price is $25, what is the percent discount?
    9·1 answer
  • Determine whether the function is proportional or nonproportional. y = 3x -
    10·1 answer
  • What does x equal in this problem
    15·1 answer
  • Help me plz <br>I will give points ​
    14·2 answers
  • Determine wether the lines given are parallel, perpendicular or neither
    6·2 answers
  • Justin and elena each launched a toy rocket into the air. the height of justin’s rocket is modeled by the equation h = –16t2 60t
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!