Question

What is the value of the logarithmic or exponential expression?

Select True or False for each statement.

Statement True False
2^(4log2(3))=81

1/2lne^3=√3

e^(3+2lne)=2e^3

Answer 1

True and False for each statement:

2^(4log2(3))=81 : TRUE

1/2lne^3=√3 : FALSE

e^(3+2lne)=2e^3 : TRUE

Step-by-step explanation:

To determine the value of the logarithmic or exponential expressions, let's evaluate each statement:

1) 2^(4log2(3)) = 81. We can rewrite this expression as 2^(log2(3^4)).

According to the property of logarithms, loga(b^c) = cloga(b), this expression simplifies to

2^(4log2(3)) = 2^(log2(81)) = 81.

Therefore, the statement is True.

2) 1/2lne^3 = √3: Using the property loga(b^c) = cloga(b), we can rewrite the expression as ln(e^(3/2)).

Since ln and e are inverse functions, ln(e^(3/2)) = 3/2.

However, 3/2 is not equal to √3.

Therefore, the statement is False.

3) e^(3+2lne) = 2e^3: We can simplify the expression using the property loga(b) + loga(c) = loga(b*c):

e^(3+2lne) = e^3*e^(2lne)

= e^3*e^2 = (e^3)^2

= 2e^3.

Therefore, the statement is True.