Question

(Help!) What is the value of the logarithmic or exponential expression?

Select True or False for each statement.

Answer 1

Using known logarithmic properties, the logarithm of a number raised to an exponent equals the exponent multiplied by the logarithm of the number. Exponential functions and natural logarithms are inverses, and logarithms can simplify multiplication and division into addition and subtraction.

Step-by-step explanation:

The value of the logarithmic or exponential expression can often be found by applying a set of known logarithmic and exponential properties. In particular:

• The logarithm of a number raised to an exponent is the product of the exponent and the logarithm of the number (TRUE).
• For exponential functions and natural logarithms, which are inverse functions to each other, we have In (ex) = x and eln x = x.
• The common logarithm (log) is the power to which 10 must be raised to equal a number (e.g., log(100) = 2).
• The logarithm of a product of two numbers is the sum of the logarithms of the two numbers (log(xy) = log(x) + log(y)).
• The logarithm of the number resulting from the division of two numbers is the difference between the logarithms of the two numbers (log(x/y) = log(x) - log(y)).