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OLga [1]
3 years ago
7

Evaluate each logarithm. Do not use a calculator. Log (125)(1/25)

Mathematics
1 answer:
svetlana [45]3 years ago
6 0

Answer:

-2/3

Step-by-step explanation:

Log125(1/25)=x

Raise each side to the base of 125

125^Log125(1/25)=125^x

1/25 = 125^x

Rewrite 25 as a power of 5  and 125 as a power of 5

1 / 5^2 = 5^3^x

The if power is in the denominator, we can bring it to the numerator by making it negative

5^-2 = 5^3^x

We know that a^b^c = a^(b*c)

5^-2 = 5^(3*x)

Since the bases are the same, the exponents are the same

-2 = 3x

Divide by 3

-2/3 = 3x/3

-2/3 =x

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The length of Rebecca’s rectangular garden was two times the width “w”. She increased the length and width of the garden so that
Damm [24]

Answer:

rebecca increased the length by 3 and the width by 2

Step-by-step explanation:

First we need to find the length and width by factorizing the expressio ofr the area;

A = 2w^2+7w+6

A = 2w^2+4w+3w+6

A = 2w(w+2)+3(w+2)

A = (2w+3)(w+2)

Since l = 2w

Length = 2w+3

width = w+2

This shows that rebecca increased the length by 3 and the width by 2

6 0
3 years ago
F ∠BAC = 17° and ∠CED = 17° are the two triangles, ΔBAC and ΔCED similar? If so, by what criterion?
diamong [38]
<span>yes, by AA criterion</span>
5 0
3 years ago
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What is AB in the figure?
sweet [91]

Answer:

Angle Bisector

Step-by-step explanation:


3 0
3 years ago
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The number of rainbow smelt in Lake Michigan had an average rate of change of −19.76 per year between 1990 and 2000. The bloater
mojhsa [17]
Let x =  number of years between 1990 and  2000.

Rainbow smelt:
Initial population = 227
Average yearly rate of change = -19.76
The linear function that models the population is
y₁ = 227 - 19.76x

Bloater fish
Initial population = 1052
Average yearly rate of change = -92.57
The linear function that models the population is
y₂ = 1052 - 92.57x

When the two populations are equal, then y₁ = y₂.
That is
227 - 19.76x = 1052 - 92.57x
(92.57 - 19.76)x = 1052 - 227
72.81x = 825
x = 11.33 years
   = 11 years, 0.33*12 months
   = 11 years, 4 months
Add x to 1990 to obtain the year April 2011.

Answer:
x = 11.33 years.
This occurs in April 2001.
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3 years ago
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