log(x)+log(2x)=5

Question

Solve for x.

Answer 1

using the log law ln(a) + ln(b) = ln(a*b),

lOG(x)+ log(2x) = log(2x^2)

log(2x^2) = 5

Take the inverse log of both sides

2x^2 = 10^5 (assuming its log base 10)

therefore x^2 = (10^5)/2

so x = sqrt((10^5)/2) =  sqrt 50,000 = 100 * sqrt(5) = 223.61 (5sf)

Answer 2

using the log law ln(a) + ln(b) = ln(a*b),

lOG(x)+ log(2x) = log(2x^2)

log(2x^2) = 5

Take the inverse log of both sides

2x^2 = 10^5 (assuming its log base 10)

therefore x^2 = (10^5)/2

so x = sqrt((10^5)/2) =  sqrt 50,000 = 100 * sqrt(5) = 223.61 (5sf)

 

(sorry i reposted it, forgot to sign in for credibility purposes before posting)