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

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Answer 1 · 2015-10-25T06:55:05

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

#[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))#