Question

To find the exact value of a logarithm, what steps should you take, and what fact can you use when dealing with the logarithm in exponential notation?

Answer 1

To find the exact value of a logarithm, follow these steps: identify the base and argument of the logarithm, write the logarithm in exponential notation, and solve for the exponent.

Step-by-step explanation:

To find the exact value of a logarithm, you can use the fact that logarithms are exponents and follow the same rules as operations involving exponents. Here are the steps to find the exact value of a logarithm:

1. Identify the base of the logarithm. For example, if you have logb(x), the base is 'b'.
2. Identify the argument of the logarithm. For example, in logb(x), the argument is 'x'.
3. Write the logarithm in exponential notation. For example, logb(x) can be written as by = x.
4. Solve for the exponent 'y' using algebraic techniques specific to the equation. For example, if you have log2(8) = y, you can rewrite it as 2y = 8. Solving this equation yields y = 3.

Using these steps, you can find the exact value of a logarithm. Remember to check your answer by substituting it back into the original logarithmic equation.