Juan Hewlett
2021-12-13
Answered

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Raymond Foley

Answered 2021-12-14
Author has **39** answers

Daniel Cormack

Answered 2021-12-15
Author has **34** answers

Let

thus, we have

Therefore,

asked 2022-06-13

Solving for x in a equation involving natural logarithms

How would I solve for x in this equation here:

$\mathrm{ln}(x)+\mathrm{ln}(1/x+1)=3$

I realize that the answer is ${e}^{3}-1$ , but I am not sure as to how to get it. Any input is appreciated.

How would I solve for x in this equation here:

$\mathrm{ln}(x)+\mathrm{ln}(1/x+1)=3$

I realize that the answer is ${e}^{3}-1$ , but I am not sure as to how to get it. Any input is appreciated.

asked 2022-09-04

Rewrite as a single log with a coefficient of one.

$(4\mathrm{ln}(x))-(3\mathrm{ln}(x))+(1/4\mathrm{ln}(x))$

$(4\mathrm{ln}(x))-(3\mathrm{ln}(x))+(1/4\mathrm{ln}(x))$

asked 2022-08-19

solve for $x$ without using softwares ${\mathrm{log}}_{\sqrt{x}}2+{\mathrm{log}}_{6}{x}^{x}=4$

Is there any nice way to solve this equation without wolfram?

${\mathrm{log}}_{\sqrt{x}}2+{\mathrm{log}}_{6}{x}^{x}=4$

Thanks.

Is there any nice way to solve this equation without wolfram?

${\mathrm{log}}_{\sqrt{x}}2+{\mathrm{log}}_{6}{x}^{x}=4$

Thanks.

asked 2022-06-20

ogarithmic inequality with different bases

I have problem with following inequality ${\mathrm{log}}_{4}5+{\mathrm{log}}_{5}6+{\mathrm{log}}_{6}7+{\mathrm{log}}_{7}8\ge 4.4$

I tried to change all logarithms to base $10$ but it didn't work

I have problem with following inequality ${\mathrm{log}}_{4}5+{\mathrm{log}}_{5}6+{\mathrm{log}}_{6}7+{\mathrm{log}}_{7}8\ge 4.4$

I tried to change all logarithms to base $10$ but it didn't work

asked 2022-05-21

Solving inequality having log

I am struggling to solve this inequality involving logarithm. How to find out values of n for which below inequality holds good:

$\frac{{\mathrm{log}}_{2}n}{n}>\frac{1}{8}$

I am struggling to solve this inequality involving logarithm. How to find out values of n for which below inequality holds good:

$\frac{{\mathrm{log}}_{2}n}{n}>\frac{1}{8}$

asked 2022-03-22

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.

asked 2022-03-15

Approximating a simple sum

Can somone help me find an assymptotic formula for n, for fixed x , for this sum , perhaps an inequality would be even better, or some bound on the error.

$\sum _{k=1}^{n}\frac{1}{\mathrm{log}\left(kx\right)}$

I need somthing better then the integral from 1 to n of ln(kx) with respect to k. Its also okay if you use special functions, like the logarithmic integral.

Can somone help me find an assymptotic formula for n, for fixed x , for this sum , perhaps an inequality would be even better, or some bound on the error.

I need somthing better then the integral from 1 to n of ln(kx) with respect to k. Its also okay if you use special functions, like the logarithmic integral.