Rules of Logarithms: Can someone explain how to do:
1) e^(2(ln)(x))
2) e^(-lnx)
I know the rules I just don't understand how they apply..
thanks!
the "rule" here is that
e^ln(k) = k
so e^(2lnx)
= e^ln(x^2)
= x^2
and
2) e^(-lnx)
= e^ln(x^-1)
= x^-1
or 1/x
This is not the trigonometry I studied in high school
Sure! Let's break down each expression step by step:
1) e^(2(ln(x)))
To simplify this expression, we'll use the property of logarithms that states log(base a) (a^x) = x. In this case, we have e^(ln(x)) raised to the power of 2.
Step 1: Recall that e^(ln(x)) is simply x. So the expression simplifies to x^2.
So, e^(2(ln(x))) can be simplified to x^2.
2) e^(-ln(x))
In this case, we'll use the property that states e^(-ln(x)) = 1 / e^(ln(x)).
Step 1: Simplify e^(ln(x)). By using the property log(base a) (a^x) = x, we know that e^(ln(x)) is just x.
Step 2: Rewrite e^(-ln(x)) as 1 / e^(ln(x)). Since we know e^(ln(x)) is x, we can rewrite this as 1 / x.
So, e^(-ln(x)) simplifies to 1 / x.
These are the step-by-step explanations of how to simplify the given expressions using the rules of logarithms.