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Nataliya [291]
3 years ago
15

Which exponential equation is equivalent to the logarithmic equation below? c = ln 2

Mathematics
1 answer:
Sophie [7]3 years ago
6 0
\text{A logarithmic lemma: } \\ \text{It follows that: } \log_a a = 1
\text{Following this property, we can see that: } a^{\log_{a} a} = a
\text{Furthermore, we can create more general properties: } a^{\log_a b} = b

c = \log_e 2 \Rightarrow e^{c} = e^{\log_e 2} \\ \text{Using our third property, we see that: } e^{c} = 2
\text{And finally, this works for any } \log_{a} b \left\{a > 0, b \in \mathbb{R}\right\}
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Step-by-step explanation:

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3 years ago
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The centers of Marathon County, Bayfield County, and Dodge County all lie along a straight road. If Marathon County is equidista
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Answer:

<em>The distance from Bayfield County to Dodge County is 974 miles.</em>

Step-by-step explanation:

Definition of equidistant: equal distance.

Bayfield                                            Marathon                                        Dodge

       +---------------------------------------------+---------------------------------------------+

                            487 miles                                         487 miles

The three centers of the counties lie along a straight line. Since Marathon County is equidistant from Bayfield County and Dodge County, then Marathon County is exactly at the midpoint of the segment from Bayfield County to Dodge County. The distances from Bayfield County to Dodge County and from Marathon County to Dodge County are equal. The distance from Bayfield County to Dodge County is

distance = 487 miles + 487 miles = 974 miles


5 0
3 years ago
In a recent year, the weather was partly cloudy 2/5 of the days. Assuming there are 365 days in a year, how many days were partl
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Devin signs a note for a discounted loan agreeing to pay $2,700 in 6 months at a discount rate of 7%. Determine the amount of th
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Answer:

discount= $94.5

Proceeds=$2605.5

Step-by-step explanation:

amount Dawin has to pay= $2700

in 6 months time

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here future value = $2700

D= discount before m months is given by

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m= 6 months, r= 7% and FV= 2700

putting values

D= \frac{2700\times 7\times 6}{1200}

solving we get

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now present value = future value - discount

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The answer is
20+4(3•2-5)+2•2=28
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