How do you solve $log(x) + log(2x) = 10$ ?

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Answer 1 · 2018-05-17T15:41:14

$color(maroon)(x = 50000sqrt2, -50000sqrt2$

$log m + log n = log (mn)$

Given : $log x + log (2x) = 10$

$:. log (x*2x) = 10$

$log (2x^2) = 10$

$2x^2 = 10^(10)$

$x^2 = 10^(10)/2$

$x = sqrt (10^(10)/2)$

$x = +-10^5/sqrt2$

$color(maroon)(x = 50000sqrt2, -50000sqrt2$

How do you solve log(x) + log(2x) = 10 log(x) + log(2x) = 10 ?