- #1
late347
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- 15
Homework Statement
$$ln(x^2)=4$$
Homework Equations
##a^{log_a(x)}=x##
##log_a(a^x)=x##
The Attempt at a Solution
ln(x^2)=4<=> ##2ln(x)=ln(4)##
<=> ##ln(x)= [ln(4)]/2##
<=> ##log_e(x)= [ln(4)]/2##
<=> ##e^{ln(4)/2}=x##
<=> ##[e^{ln(4)}]^{1/2}##
<=> ##sqrt(e^{ln(4)})##
here I was a little bit confused about, how can we know what the thing inside the square root will be, in order to take the square root from it?
What do we know about the value of (e^{ln(4)}) so the square root of it can be taken?
I understand the other formula which was
##log_a(a^x)=x##
obviously the ##log_a(a^x)## asks us what exponent is the correct one, when you want to raise a to the exponent of something, such that the result will become a^x. The answer is x for the exponent.