Final Answer:
The equation m⁻⁷ = n rewritten in logarithmic form is logₘ(n) = -7.
Step-by-step explanation:
To rewrite the equation m⁻⁷ = n in logarithmic form, we can use the definition of a logarithm. The logarithmic form of an equation is written as logₐ(b) = c, where a is the base, b is the result of the exponentiation, and c is the exponent. In this case, we rewrite m⁻⁷ = n as logₘ(n) = -7, where m is the base, n is the result, and -7 is the exponent.
In this logarithmic form, the base (m) represents the number being raised to a power, the result (n) is the value obtained from raising the base to a power, and the exponent (-7) indicates the power to which the base must be raised to obtain the result. Therefore, logₘ(n) = -7 represents the logarithmic form of the given equation m⁻⁷ = n.
Understanding logarithmic forms of equations is essential in solving various mathematical problems and applications in fields such as science, engineering, and finance. It allows for a better understanding of exponential relationships and provides a powerful tool for solving complex equations involving exponents.
By rewriting equations in logarithmic form, we can manipulate and solve them more effectively, making logarithms an important concept in mathematics with wide-ranging practical applications.