Saturday, April 11, 2020

2020/13) Solve $2\log_2(x+15) - \log_2x = 6$

We have
$2\log_2(x+15) - \log_2x = \log_2(x+15)^2 - \log_2(x) = \log_2\frac{(x+15)^2}{x} = 6$
Or $\frac{(x+15)^2}{x} = 2^6= 64$
Or $(x+15)^2 = 64x$
Or $x^2+30x+225-64x=0$
Or $x^2-34x+ 225=0$
Or $(x-25)(x-9)= 0$ So x = 25 or 9 

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