Find $x$ in $\mathrm{log}{x}^{2}=(\mathrm{log}x{)}^{2}$

I couldn't find x.

I couldn't find x.

Frank Day
2022-07-02
Answered

Find $x$ in $\mathrm{log}{x}^{2}=(\mathrm{log}x{)}^{2}$

I couldn't find x.

I couldn't find x.

You can still ask an expert for help

Bruno Dixon

Answered 2022-07-03
Author has **14** answers

$\mathrm{log}{x}^{2}=(\mathrm{log}x{)}^{2}\phantom{\rule{0ex}{0ex}}2\mathrm{log}x=(\mathrm{log}x{)}^{2}\phantom{\rule{0ex}{0ex}}\mathrm{log}x(\mathrm{log}x-2)=0\phantom{\rule{0ex}{0ex}}\mathrm{log}x=0\to x=1\phantom{\rule{0ex}{0ex}}\mathrm{log}x=2\to x={10}^{2}$

Patatiniuh

Answered 2022-07-04
Author has **5** answers

Hint: Note that

$\mathrm{log}{x}^{2}=2\mathrm{log}x$

for all $x>0.$ Now use the substitution $u=\mathrm{log}x$ to get

$2u={u}^{2}.$

Solve for $u,$ then solve for $x.$

$\mathrm{log}{x}^{2}=2\mathrm{log}x$

for all $x>0.$ Now use the substitution $u=\mathrm{log}x$ to get

$2u={u}^{2}.$

Solve for $u,$ then solve for $x.$

asked 2022-05-21

Relating an expression to two similar ones

Is it possible to express C solely in terms of A and B, where

$A={\displaystyle \frac{m}{x+z}},B={\displaystyle \frac{n}{y+z}},C={\displaystyle \frac{m+n}{x+y+z}}$

and $m,n,x,y,z>0\text{}?$

If not, how close can I get?

Is it possible to express C solely in terms of A and B, where

$A={\displaystyle \frac{m}{x+z}},B={\displaystyle \frac{n}{y+z}},C={\displaystyle \frac{m+n}{x+y+z}}$

and $m,n,x,y,z>0\text{}?$

If not, how close can I get?

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How exactly do I add $\frac{1}{680}+\frac{1}{940}+\frac{1}{1200}$ to get theanswer, which is 296.93?

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Fraction and Decimal: Reciprocal of x's non-integer

The reciprocal part of $x$'s non-integer decimal part equals $x+1$, and $x>0$. What is $x$?

Solution: I tried this way-

Let's $n$= integer part of $x$

$1/x-n=x+1$

or, $1=(x-n)(x+1)$

or, $1={x}^{2}+x-nx-n$

or, ${x}^{2}+(1-n)x-(n+1)=0$

but, stucked here. Is there any other way?

The reciprocal part of $x$'s non-integer decimal part equals $x+1$, and $x>0$. What is $x$?

Solution: I tried this way-

Let's $n$= integer part of $x$

$1/x-n=x+1$

or, $1=(x-n)(x+1)$

or, $1={x}^{2}+x-nx-n$

or, ${x}^{2}+(1-n)x-(n+1)=0$

but, stucked here. Is there any other way?

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How do you convert 0.625 into a percent and fraction?

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Summation and Patterns Question

I have a really urgent question. Today i was looking at this Pattern (Using fractions) :

$\frac{1}{1\ast 3}+\frac{1}{3\ast 5}+\frac{1}{5\ast 7}+\frac{1}{7\ast 9}+...$=? The pattern is $\frac{n}{2n+1}$. I was wondering if you could do a summation formula, in which the end term is infinite. Thanks for the help!

I have a really urgent question. Today i was looking at this Pattern (Using fractions) :

$\frac{1}{1\ast 3}+\frac{1}{3\ast 5}+\frac{1}{5\ast 7}+\frac{1}{7\ast 9}+...$=? The pattern is $\frac{n}{2n+1}$. I was wondering if you could do a summation formula, in which the end term is infinite. Thanks for the help!

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how to convert decimals into fractions

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Nested fractional denominator(up to infinity)calculation

Question:

$$4+{\displaystyle \frac{1}{2+{\displaystyle \frac{1}{1+{\displaystyle \frac{1}{3+{\displaystyle \frac{1}{1+{\displaystyle \frac{1}{2+{\displaystyle \frac{1}{8+{\displaystyle \frac{1}{\ddots}}}}}}}}}}}}}}=\sqrt{A}$$

Find the positive integer A in the equation above.

Details and assumptions

The pattern repeats 2, 1, 3, 1, 2, 8 infinitely, but 4 comes only once, i.e., at the beginning.

Question:

$$4+{\displaystyle \frac{1}{2+{\displaystyle \frac{1}{1+{\displaystyle \frac{1}{3+{\displaystyle \frac{1}{1+{\displaystyle \frac{1}{2+{\displaystyle \frac{1}{8+{\displaystyle \frac{1}{\ddots}}}}}}}}}}}}}}=\sqrt{A}$$

Find the positive integer A in the equation above.

Details and assumptions

The pattern repeats 2, 1, 3, 1, 2, 8 infinitely, but 4 comes only once, i.e., at the beginning.