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eimsori [14]
3 years ago
11

How do you determine the base when solving for x by converting to a log?

Mathematics
1 answer:
worty [1.4K]3 years ago
8 0

$x=\frac{\ln \left(\frac{3}{2}\right)}{4 \ln (1.0125)}

Solution:

Given expression:

$(1.0125)^{4 x}=\frac{3}{2}

To solve the expression:

$(1.0125)^{4 x}=\frac{3}{2}

<em>If f(x) = g(x) then ln(f(x)) = ln(g(x)).</em>

Using the above condition, we can write

$\ln \left(1.0125^{4 x}\right)=\ln \left(\frac{3}{2}\right)

Apply log rule: \log _{a}\left(x^{b}\right)=b \cdot \log _{a}(x)

$4 x \ln (1.0125)=\ln \left(\frac{3}{2}\right)

Divide both side of the equation by 4 \ln (1.0125).

$\frac{4 x \ln (1.0125)}{4 \ln (1.0125)}=\frac{\ln \left(\frac{3}{2}\right)}{4 \ln (1.0125)}

$x=\frac{\ln \left(\frac{3}{2}\right)}{4 \ln (1.0125)}

The answer is x=\frac{\ln \left(\frac{3}{2}\right)}{4 \ln (1.0125)}.

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3 years ago
Can anyone help me on this problem? Please it doesn’t make sense to me...
Sav [38]

Answer:

6

Step-by-step explanation:

Cost per item is found by dividing the cost by the number of items. If the woman bought n items for $120, the cost of each item is $120/n. If the woman bought 24 more items, n+24, at the same price, then the cost per item is $120/(n+24). The problem statement tells us this last cost is $16 less than the first cost:

120/(n+24) = (120/n) -16

Multiplying by n(n+24) gives ...

120n = 120(n+24) -16(n)(n+24)

0 = 120·24 -16n^2 -16·24n . . . . . . subtract 120n and collect terms

n^2 +24n -180 = 0 . . . . . . . . . . . . . divide by -16 to make the numbers smaller

(n +30)(n -6) = 0 . . . . . . . . . . . . . . factor the quadratic

The solutions to this are the values of n that make the factors zero: n = -30, n = 6. The negative value of n has no meaning in this context, so n=6 is the solution to the equation.

The woman bought 6 items.

_____

Check

When the woman bought 6 items for $120, she paid $120/6 = $20 for each of them. If she bought 6+24 = 30 items for the same money, she would pay $120/30 = $4 for each item. That amount, $4, is $16 less than the $20 she paid for each item.

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4 years ago
Firefly211 what is the length to memphis to Alaska
Natalija [7]
Hello,

The length from Memphis to Alaska is approximately 3,946 miles.

Hope this helps!

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Answer:

The hypothesis test is right-tailed

Step-by-step explanation:

To identify a one tailed test, the claim in the case study tests for the either of the two options of greater or less than the mean value in the null hypothesis.

While for a two tailed test, the claim always test for both options: greater and less than the mean value.

Thus given this: H0:X=10.2, Ha:X>10.2, there is only the option of > in the alternative claim thus it is a one tailed hypothesis test and right tailed.

A test with the greater than option is right tailed while that with the less than option is left tailed.

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3 years ago
Division of fractions
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Answer:

The first step to dividing fractions is to find the reciprocal (reverse the numerator and denominator) of the second fraction. Next, multiply the two numerators. Then, multiply the two denominators. Finally, simplify the fractions if needed.

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