Mathematics: Ineed a solution[tex]2log_{x}25 - 3 log_{25}x = 1[/tex]

Ineed a solution[tex]2log_{x}25 - 3 log_{25}x - id22532511674482, willveloz4

Ответ:

Raewolf25

15.03.2022

Mathematics

Given
$2log_x(25)-3log_{25}(x)=1$

first, convert

to base 25 to match the other term.
2log_x(25)

$=2log_{25}(25)/log_{25}(x)$
$=2*1/log_{25}(x)$

Substitute above identity into original equation:
$2/log_{25}(x)-3log_{25}(x)=1$

Use substiution $u=log_{25}(x)$
above equation becomes
2/u-3u=1
multiply by u and solve for u:
3u^2+u-2=0

=> u=2/3 or u=-1

case A:. u=2/3 =>
$log_{25}(x)=2/3 = 25^{2/3}=x$ =>
$x=25^{2/3} =8.54987973338348 (approx.)$

case B: u=-1 =>
log_25(x)=-1

which does not give a real solution, so reject.

See graph below for confirmation of solution.
Ineed a solution<img src=

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Ответ:

bowtie123

25.01.2020

Mathematics

Step-by-step explanation:

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Ineed a solution $2log_{x}25 - 3 log_{25}x = 1$

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