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bekas [8.4K]
3 years ago
8

Find the Domain of the following exponential and logarithmic equations and solve them:

Mathematics
1 answer:
kakasveta [241]3 years ago
5 0

The base of a logarithm should always be positive and can't be equal to 1, so the domain is 0 < <em>x</em> < 1 or <em>x</em> > 1.

\log_{\frac1x}243=5

Write both sides as powers of 1/<em>x</em> :

\left(\dfrac1x\right)^{\log_{\frac1x}243}=\left(\dfrac1x\right)^5

Recall that a^{\log_ab}=b, so that

243=\left(\dfrac1x\right)^5

243=\dfrac1{x^5}

x^5=\dfrac1{243}

Take the 5th root of both sides, recalling that 3⁵ = 243, so

x=\sqrt[5]{\dfrac1{243}}=\boxed{\dfrac13}

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Answer:

w = 12

Step-by-step explanation:

3w = 11 + 25

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w = 12

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B. 28 hours

Step-by-step explanation:

GIVEN :- <em>Time taken by family to travel 600 km is 8 hours</em>

CALCULATIONS :-

<em>To calculate the time to travel 2100 km, we need to calculate distance traveled in 1 hour</em>

<em>Distance traveled in 1 hour = 600 km ÷ 8</em>

<em>                                              = 75 km</em>

<em>Time required to travel 2100 km = 2100 ÷ 75</em>

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Therefore time required to travel 2100 km is 28 hours.


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3 years ago
If a is half b , and b is twice c , then a:c=​
faust18 [17]

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2205

Step-by-step explanation:

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x = 7

Step-by-step explanation:

According to the side-splitter theorem, the two sides of the triangle is divided proportionally if the line that intersects both sides is parallel to the third side of the ∆.

Therefore, based on this theorem, we would have the following:

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