High School

If [tex]\log c = -399.699[/tex], give the value of [tex]c[/tex] in scientific notation. The value of [tex]c[/tex] is small but does not equal zero.

A. [tex]1.4 \times 10^{-173}[/tex]
B. [tex]1.7 \times 10^{-173}[/tex]
C. [tex]2.1 \times 10^{-173}[/tex]
D. [tex]2.5 \times 10^{-173}[/tex]

Answer :

Final answer:

The value of c is small but does not equal zero: 1.7 x 10¹⁷³ thus the corrrect option is b.

Explanation:

To find the value of c in scientific notation, we need to understand that logarithms provide a way to represent numbers in a condensed form. The given equation log c = -399.699 indicates that 10 raised to the power of -399.699 equals c. Thus, c can be expressed in scientific notation as c = 10^(-399.699). By converting this expression to standard scientific notation, we get c ≈ 1.7 x 10¹⁷³, which matches option B.(option b)

Taking the antilogarithm of -399.699 gives us the value of c. Using the properties of logarithms, we know that 10 raised to the power of -399.699 is equivalent to c. Thus, c ≈ 10^(-399.699). To express this value in scientific notation, we rewrite it as 1.7 x 10¹⁷³. Therefore, option B, 1.7 x 10¹⁷³, accurately represents the value of c in scientific notation.(option b)

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