What is x if ln(x^2) + ln(x^3) + 2 =0?

1 Answer
Oct 25, 2015

x=root(5)(1/e^2)

Explanation:

[1]" "lnx^2+lnx^3+2=0

Property: log_bm+log_bn=log_b(mn)

[2]" "ln(x^2x^3)+2=0

[3]" "ln(x^5)+2=0

Transfer 2 to the other side.

[4]" "ln(x^5)=-2

[5]" "log_e(x^5)=-2

Convert to exponential form.

[6]" "hArre^-2=x^5

[7]" "root(5)(1/e^2)=root(5)(x^5)

[8]" "color(blue)(x=root(5)(1/e^2))