Match the logarithm in Column I with its value in Column II....

Match the logarithm in Column I with its value in Column II. Remember that $\log _{a} x$ is the exponent to which a must be raised in order to obtain $x.$ $\mathbf{I}$ (a) $\log _{2} 16$ (b) $\log _{3} 1$ (c) $\log _{10} 0.1$ (d) $\log _{2} \sqrt{2}$ (e) $\log _{e} \frac{1}{e^{2}}$ (f) $\log _{1 / 2} 8$ $\mathbf{II}$ A. 0 B. $\frac{1}{2}$ C. 4 D. $-3$ E. $-1$ F. $-2$

Match the logarithm in Column I with its value in Column II. Remember that $\log _{a} x$ is the exponent to which a must be raised in order to obtain $x.$
$\mathbf{I}$
(a) $\log _{2} 16$
(b) $\log _{3} 1$
(c) $\log _{10} 0.1$
(d) $\log _{2} \sqrt{2}$
(e) $\log _{e} \frac{1}{e^{2}}$
(f) $\log _{1 / 2} 8$
$\mathbf{II}$
A. 0
B. $\frac{1}{2}$
C. 4
D. $-3$
E. $-1$
F. $-2$

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Key Concepts

Logarithms with Fractional and Root Values

When dealing with logarithms that involve fractional expressions or radicals, it is helpful to express these numbers as exponents. This conversion simplifies the process of matching them to the corresponding exponent values.

Logarithms Involving Reciprocal Values

Evaluating logarithms where the argument is a reciprocal or a fraction often results in negative values. This is due to the negative exponents required to represent reciprocals in exponential form.

Definition of Logarithms

A logarithm log?(x) represents the exponent to which the base a must be raised to produce the number x. This definition forms the core concept for understanding and solving logarithmic problems.

Properties of Exponents

Comprehending the rules of exponents is essential when working with logarithms, as these rules allow us to rewrite numbers (such as powers and roots) in a form that makes evaluating logarithms straightforward.

Logarithm of 1

One of the fundamental properties of logarithms is that log?(1) equals 0 for any valid base a, because any nonzero number raised to the power of 0 equals 1.

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