4 years ago

Need help on question 8 asap

1 answer:

6 0

A) 8 chocolate chip cookies

B) The ratio of sugar to oatmeal is 2:3 because there are 12 sugar and 18 oatmeal. 12/18 simplified is 2/3.

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I need a solution<br><img src="https://tex.z-dn.net/?f=2log_%7Bx%7D25%20-%203%20log_%7B25%7Dx%20%3D%201" id="TexFormula1" title=

Korvikt [17]

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

first, convert $2log_x(25)$ 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.