I Know You Will Avoid It, But Solve. - Education

I Know You Will Avoid It, But Solve. - Education - Nairaland

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I Know You Will Avoid It, But Solve. by ifada123(op): 12:56pm On Apr 09, 2019

X^logx=10000x^3

With workings

Re: I Know You Will Avoid It, But Solve. by Martinez39(m): 4:54pm On Apr 09, 2019*

ifada123:
X^logx=10000x^3

With workings

Taking the common logarithms of both sides :
log x^{log x} = log (10⁴ × x³)
Using the properties of logarithms
(log x)(log x) = log 10⁴ + log x³
(log x)² = 4 + 3log x ----- an equation quadratic in form
If u = log x then u² = 4 + 3u
Using the quadratic formula to solve u² - 3u - 4 = 0
u = log x = 4 or u = log x = -1
ie. x = 10⁴ or x = 10^-1

On checking, the solution set is, {10⁴, 10^-1}

1 Like

Re: I Know You Will Avoid It, But Solve. by dejt4u(m): 7:38pm On Apr 09, 2019

Martinez39:
Taking the common logarithms of both sides :
log x^{log x} = log (10⁴ × x³)
Using the properties of logarithms
(log x)(log x) = log 10⁴ + log x³
(log x)² = 4 + 3log x³ ----- an equation quadratic in form
If u = log x then u² = 4 + 3u
Using the quadratic formula to solve u² - 3u - 4 = 0
u = log x = 4 or u = log x = -1
ie. x = 10⁴ or x = 10^-1

On checking, the solution set is, {10⁴, 10^-1}

You made a mistake here. it didn't affect your workings though. a typographical error I think
(log x)² = 4 + ~~3log x³~~

It should be (log x)² = 4 + 3log x

You did well. keep it up

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Re: I Know You Will Avoid It, But Solve. by Martinez39(m): 7:39pm On Apr 09, 2019

dejt4u:
You made a mistake here. it didn't affect your workings though. a typographical error I think
(log x)² = 4 + ~~3log x³~~

It should be (log x)² = 4 + 3log x

Thanks. It was a typo.

Re: I Know You Will Avoid It, But Solve. by dejt4u(m): 7:40pm On Apr 09, 2019

Martinez39:
Thanks. It was a typo.

yes.. well done

Re: I Know You Will Avoid It, But Solve. by ifada123(op): 8:39pm On Apr 09, 2019

Martinez39:
Taking the common logarithms of both sides :
log x^{log x} = log (10⁴ × x³)
Using the properties of logarithms
(log x)(log x) = log 10⁴ + log x³
(log x)² = 4 + 3log x ----- an equation quadratic in form
If u = log x then u² = 4 + 3u
Using the quadratic formula to solve u² - 3u - 4 = 0
u = log x = 4 or u = log x = -1
ie. x = 10⁴ or x = 10^-1

On checking, the solution set is, {10⁴, 10^-1}

√√√√√√√√√√
correct,

Re: I Know You Will Avoid It, But Solve. by ifada123(op): 10:25am On Apr 10, 2019

Get ready more shape questions loading....
I remain your shape lover
Mr Shape

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