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I Know You Will Avoid It, But Solve. by ifada123: 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 xlog 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}

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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 xlog 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: 8:39pm On Apr 09, 2019
Martinez39:


Taking the common logarithms of both sides :
log xlog 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: 10:25am On Apr 10, 2019
Get ready more shape questions loading....
I remain your shape lover
Mr Shape

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