3 years ago

Helpppppppppppppppppppp mathhhhhhhhhhh

1 answer:

6 0

Since it's a local (a possible branch) hardware store, it's POSSIBLE BUT VERY UNLIKELY:
PROOF: Assume 100 clients/day are buying from this store, that means,
3,600 customer a month or 43,200 clients a year. The one-millionth customer will occur after 1,000,000/43,200 = 23 years. or it will be after 46 years if the average customer is 50/day. So it is possible but MOST UNLIKELY

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Solve 10e^2x - 5 =23^x for x.

yawa3891 [41]

$10e^{2x}-5=23e^x\qquad\text{subtract}\ 23e^x\ \text{from both sides}\\\\10e^{2x}-23e^x-5=0\\\\10(e^x)^2-23(e^x)-5=0\\\\\text{substitution:}\ e^x=t > 0\\\\10t^2-23t-5=0\\\\10t^2-25t+2t-5=0\\\\5t(2t-5)+1(2t-5)=0\\\\(2t-5)(5t+1)=0\iff2t-5=0\ \vee\ 5t+1=0\\\\2t=5\ \vee\ 5t=-1\\\\t=\dfrac{5}{2} > 0\ \vee\ t=-\dfrac{1}{5} < 0\\\\\text{therefore}\ e^x=\dfrac{5}{2}\to\ln e^x=\ln\left(\dfrac{5}{2}\right)\\\\\boxed{x=\ln\left(\dfrac{5}{2}\right)}$