In Exercises 9–20, write each equation in its equivalent logarithmic form. 13^2 = x

Verified step by step guidance

1. Identify the components of the exponential equation: the base is 13, the exponent is 2, and the result is x.
2. Recall the definition of a logarithm: if $a^b=c$, then ${\log }_a(c)=b$.
3. Apply the definition to the given equation ${13}^2=x$.
4. Rewrite the equation in logarithmic form: ${\log }_{13}(x)=2$.
5. Verify that the rewritten equation correctly represents the original exponential relationship.

Key Concepts

Exponential Equations

Exponential equations are mathematical expressions where a variable is in the exponent. In the equation 13^2 = x, 13 is the base raised to the power of 2, resulting in x. Understanding how to manipulate these equations is crucial for converting them into logarithmic form.

Logarithmic Form

Logarithmic form is a way to express exponential equations using logarithms. The equation a^b = c can be rewritten as log_a(c) = b. This transformation is essential for solving equations involving exponents and helps in understanding the relationship between the base, exponent, and result.

Base of a Logarithm

The base of a logarithm is the number that is raised to a power to obtain a given number. In the context of the equation 13^2 = x, the base is 13. Recognizing the base is important when converting to logarithmic form, as it determines how the logarithm is expressed.