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Sholpan [36]
3 years ago
7

Evaluate the logarithmic expression Log subscript5^25 +log subscript 5^625/logsubscript5^100. The value of the expression, round

ed to the nearest hundredth, is____.
Mathematics
1 answer:
Lady bird [3.3K]3 years ago
3 0
Hello !
Here are some rules for logarithms :    log ₐ b = n ⇔ aⁿ = b
                                                             log ₐ aⁿ = n
                                                             log ₐ (b·c) = logₐ b + log ₐ  c                                                                                                                  
                                                             log ₐ bⁿ = n· log ₐ b                                        ____________________________________________________
25=5²
625=5⁴
100 = 5² · 2²
____________________________________________________



(log₅ 25 + log₅ 625) / log₅100 =
 (log₅ 5²+ log₅ 5⁴) / log₅ (5² · 2²) =
 (log₅ 5²+ log₅ 5⁴) /( log₅ 5² + log₅ 2²) =
(2 + 4)/(2+log₅ 2² ) =
 6/ (2+2·log₅2)=
6/2 + 6/ (2·log₅2) =

3+ 3/log₅2
log₅2 = 0.5

So 3+ 3/log₅2 = 3 + 3/0.5 =3 + 6 = 9 

Answer : 9






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Step-by-step explanation:

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2 years ago
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Answer:

Step-by-step explanation:

1. 30

2. 23

3. 8

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6 0
3 years ago
526 less than ————— is 200.
charle [14.2K]

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5 0
3 years ago
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qwelly [4]

Answer:

180 cm²

Step-by-step explanation:

From inspection of the diagram, the surface area is made up of the area of 4 congruent triangles and the area of one square.

Area of a square = x² (where x is the length of one side)

⇒ area of the square = 6² = 36 cm²

Area of a triangle = 1/2 x base x height

⇒ area of one triangle = 1/2 x 6 x 12 = 36 cm²

Total surface area = 4 x area of one triangle + area of the square

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                               = 180 cm²

5 0
2 years ago
Read 2 more answers
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