An equation that involves exponential growth.
An equation that measures angles in trigonometric functions.
A logarithmic equation is an equation that involves a logarithm of an expression set equal to a number or another expression.
An equation that solves for the slope of a line.
Use the Pythagorean Theorem to find the solution.
To solve \( \log_b(x) = c \), rewrite the equation in exponential form as \( x = b^c \).
Rewrite the equation as \( c = b \cdot x \).
Factor the polynomial to find the solution.
The base and argument must both be negative.
The base must be positive and not equal to 1, and the argument must be positive.
Both the base and argument can be zero.
The base and argument must both be even numbers.
By integrating the functions involved.
Properties such as the product, quotient, and power rules can simplify expressions and isolate the variable.
By converting them to algebraic equations.
By applying statistical methods.
\( \log_b(M/N) = \log_b(M) \cdot \log_b(N) \)
\( \log_b(M+N) = \log_b(M) - \log_b(N) \)
The product rule states \( \log_b(MN) = \log_b(M) + \log_b(N) \).
\( \log_b(M^n) = n + \log_b(M) \)
The power rule states \( \log_b(M^n) = n \cdot \log_b(M) \).
The power rule states \( \log_b(M^n) = n \cdot M \).
The power rule states \( \log_b(M) = n \cdot M \).
The power rule states \( \log_b(M^n) = \frac{1}{n} \cdot \log_b(M) \).
The quotient rule states \( \log_b(M/N) = \log_b(M) - \log_b(N) \).
The quotient rule states \( \log_b(M/N) = \log_b(M) + \log_b(N) \).
The quotient rule states \( \log_b(M+N) = \log_b(M) \cdot \log_b(N) \).
The quotient rule states \( \log_b(M \cdot N) = \log_b(M) - \log_b(N) \).
By the one-to-one property, set \( x^2 = 9 \), solve for \( x \): \( x = 3 \) or \( x = -3 \) (considering restrictions).
Use the difference of squares method to solve for x.
Factor \( x^2 \) and recombine terms.
Rewrite as an equation with base e and solve.
Because solutions from squaring logs always add more variability.
Extraneous solutions occur due to taking roots and combining logs that might not hold under original restrictions.
Extraneous solutions occur because logs are not defined for negative numbers.
They simply arise from solving any algebraic equations.
\( \log_b(x) = \log(x) - \log(b) \)
\( \log_b(x) = \log(x) - \log(b) \cdot 2 \)
The change of base formula is \( \log_b(x) = \frac{\log_k(x)}{\log_k(b)} \), for any positive k.
\( \log_b(x) = \log_k(x) + \log_k(b) \)