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zmey [24]
3 years ago
13

Consider the logarithms base 5. For each logarithmic expression below, either calculate the value of the expression or explain w

hy the expression does not make sense.
log5(3125)
Mathematics
1 answer:
Tom [10]3 years ago
8 0

Answer:

log₅(3125) = 5

Step-by-step explanation:

Given:

log₅(3125)

Now,

using the property of log function that

logₐ(b) = \frac{\log(b)}{\log(a)}

thus,

Therefore, applying the above property, we get

⇒ \frac{\log(3125)}{\log(5)}   (here log = log base 10)

now,

3125 = 5⁵

thus,

⇒  \frac{\log(5^5)}{\log(5)}

Now,

we know from the properties of log function that

log(aᵇ) = b × log(a)

therefore applying the above property we get

⇒ \frac{5\log(5)}{\log(5)}

or

⇒ 5

Hence,

log₅(3125) = 5

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Is 7/9 a rational number ?
zzz [600]

Answer:

Yes.

Step-by-step explanation:

Rational numbers can be represented as fractions with integers. The denominator must not equal 0.

\frac{7}{9} is already in this form. This means that it's a rational number.

Hope this helps.

8 0
3 years ago
I need help with this please help me​
jarptica [38.1K]

k equals negative 4 k=-4

3 0
2 years ago
Read 2 more answers
Sean is getting balloons for his grandfather's birthday party. He wants each balloon string to be 9 feet long. At the party stor
atroni [7]

Answer:

198 yards

Step-by-step explanation:

Sean wants the sting of each balloon to be 9 feet, and he wants to get a total of 66 balloons.

The total length of stings required for 66 balloons would be;

total length of balloon strings = 66 x 9 feet

                                                 = 594 feet

But the string is sold by the yard at the store.

So that,

1 yard = 36 inches = 3 feet

x yard = 594 feet

Thus,

x = \frac{594}{3}

  = 198 yards

x = 198 yards

Therefore, the total length of string that Sean would need is 198 yards.

3 0
2 years ago
I need help with the rest of these
Anit [1.1K]

Answer:

Step-by-step explanation:

5) 2 4/9

= 22/9

= 2.4444......

7) -1 5/6

= - 11/6

= - 1.8333.....

2) -2/11

= - 5.5

4) 1/3

= 0.3333......

6) - 13/6

= - 2.166666667

8) 13/99

= 0.1313131313......

7 0
3 years ago
Laws of cosines!!! find B round to the nearest tenth!!!! second time posting this help ASAP!!!​
Nookie1986 [14]

Answer:

32.7°

Step-by-step explanation:

Use the formula for law of cosines, for this question we need so solve for angle B, so use...

b² = a² + c² - 2(a)(c)Cos B

We are given a, b, and c, so plug them in...

55² = 90² + 50² - 2(90)(50)Cos B

Now simplify...

3,025 = 8100 + 2500 - (9000)Cos B

   -7,575 = -(9000)Cos B   (subtract 8100 and 2500 from both sides)  

   

       0.841666667 = Cos B    (divide both sides by -9000)

       Cos^(-1) 0.841666667 = B  (use cosine inverse function on calculator)

          32.68346376° = B

           32.7° = B

 

3 0
3 years ago
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