How do I solve this equation using common logarithms?

$\mathrm{log}x=1-\mathrm{log}(x-3)$

Janessa Olson
2022-07-05
Answered

Solving this logarithm equation?

How do I solve this equation using common logarithms?

$\mathrm{log}x=1-\mathrm{log}(x-3)$

How do I solve this equation using common logarithms?

$\mathrm{log}x=1-\mathrm{log}(x-3)$

You can still ask an expert for help

asked 2021-08-11

Please, rewrite and simplify, if possible, the given logarithms

a)$\mathrm{ln}8$ in terms of base 2 logarithms

b)${\mathrm{log}}_{\frac{1}{2}}4$ in terms of base 2 logarithms

c)${\mathrm{log}}_{2}1000$ in terms of common logarithms

d)${\mathrm{log}}_{2}\left({e}^{2}\right)$ in terms of natural logarithms

a)

b)

c)

d)

asked 2022-04-11

Use the properties of logarithms to write each expression as a single term.

a. $\mathrm{ln}\left[\right(x+3)-\mathrm{ln}(x-1\left)\right]$

b. $\frac{1}{2}{\mathrm{log}}_{7}(2x-3)+{\mathrm{log}}_{7}x-{\mathrm{log}}_{7}q$

asked 2022-07-17

How do you solve a equation by converting to logarithm form for the problem $3{e}^{x-4}+2=83$?

$3{e}^{x-4}+2=83$ I understand converting logarithms but i dont understand how to convert e into log form and solve. help would be deeply appreciated.

$3{e}^{x-4}+2=83$ I understand converting logarithms but i dont understand how to convert e into log form and solve. help would be deeply appreciated.

asked 2022-04-05

Equation $\mathrm{log}({x}^{2}+2ax)=\mathrm{log}(4x-4a-13)$ has only one solution; then exhaustive set of values of $a$ is

asked 2022-04-07

I'm quite ashamed that I'm at a math-related course at the university and I'm stuck. I can't solve at all this equation:

$n=8{\mathrm{log}}_{2}\left(n\right).$

I have tried applying the log property so it becomes$2}^{n}={2}^{8n$

Besides that this didn't help me, I'm not even sure if I applied right the property that says$x={\mathrm{log}}_{2}\left(y\right)\Rightarrow {2}^{x}=y$

Thanks in advance! Best Regards,

I have tried applying the log property so it becomes

Besides that this didn't help me, I'm not even sure if I applied right the property that says

Thanks in advance! Best Regards,

asked 2022-03-18

Apparently cannot be solved using logarithms

This equation clearly cannot be solved using logarithms.

$3+x=2\left({1.01}^{x}\right)$

Now it can be solved using a graphing calculator or a computer and the answer is$x=-1.0202$ and $x=568.2993.$

But is there any way to solve it algebraically/algorithmically?

This equation clearly cannot be solved using logarithms.

Now it can be solved using a graphing calculator or a computer and the answer is

But is there any way to solve it algebraically/algorithmically?

asked 2022-08-22

Trouble evaluating the sum involving logarithm

I was trying to solve this problem: Closed form for ${\int}_{0}^{1}\mathrm{log}\mathrm{log}(\frac{1}{x}+\sqrt{\frac{1}{{x}^{2}}-1})\mathrm{d}x$

In the procedure I followed, I came across the following sum:

$\sum _{k=1}^{\mathrm{\infty}}(-1{)}^{k-1}k(\frac{\mathrm{ln}(2k+1)}{2k+1}-\frac{\mathrm{ln}(2k-1)}{2k-1})$

I cannot think of any approaches which would help me in evaluating the sum.

Any help is appreciated. Thanks!

I was trying to solve this problem: Closed form for ${\int}_{0}^{1}\mathrm{log}\mathrm{log}(\frac{1}{x}+\sqrt{\frac{1}{{x}^{2}}-1})\mathrm{d}x$

In the procedure I followed, I came across the following sum:

$\sum _{k=1}^{\mathrm{\infty}}(-1{)}^{k-1}k(\frac{\mathrm{ln}(2k+1)}{2k+1}-\frac{\mathrm{ln}(2k-1)}{2k-1})$

I cannot think of any approaches which would help me in evaluating the sum.

Any help is appreciated. Thanks!