Examine whether the series

kuCAu
2021-08-18
Answered

Examine whether the series

You can still ask an expert for help

aprovard

Answered 2021-08-19
Author has **94** answers

Notice that, for all

Also note that

The given series is convergent by comparison test.

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Solve the exponential equation ${10}^{x}=8.07$ . Express the solution set in terms of natural logarithms or common logarithms.Then use a calculator to obtain a decimal approximation, correct to two decimal places, for the solution.

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How to prove derivative of logarithm with base $b$ ?

I learned how to derive a logarithm with any base. This is the formula:

$\frac{d}{dx}{\mathrm{log}}_{b}x=\frac{1}{x\mathrm{ln}b}$

How can it be proved?

I learned how to derive a logarithm with any base. This is the formula:

How can it be proved?

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The One-to-One Property of natural logarithms states that if ln x = ln y, then ________.

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How should I calculate the Lebesgue integral of logarithm function from zero to infinity?

Does the area under the$\mathrm{ln}\left(x\right)$ in $(0,+\mathrm{\infty})$ is measurable? If yes, how can I calculate it?

Does the area under the

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Find the exact value of the logarithmic expression $\mathrm{ln}\left(\frac{1}{\sqrt{e}}\right)$ without using a calculator.If this is not possible, state the reason.

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Is showing $\underset{z\to \mathrm{\infty}}{lim}{(1+\frac{1}{z})}^{z}$ exists the same as $\underset{n\to \mathrm{\infty}}{lim}(1+\frac{1}{n})$ n exists

asked 2022-03-24

Hey guys so i'm trying to turn this equation into it's sum/difference logarithm. However, the part that messes me up is turning the bottom of the fraction

${\mathrm{log}\left(\frac{{x}^{2}+2x+1}{{x}^{2}-3x+2}\right)}^{2}.$

I think it will turn into this:

$4\mathrm{log}(x+1)-2(\mathrm{log}(x-1)+\mathrm{log}(x-2)),$

but I don't want it to be$(x-1)}^{2$ times $(x-2)}^{2$ . How do I solve it so it's $\left((x-1)(x-2)\right)}^{2$ ?

I think it will turn into this:

but I don't want it to be