Final answer:
To solve log = log equations, set the arguments equal and solve for the variable. For log = number equations, convert the logarithmic form to an exponential form and then solve for the variable. Both types of equations can be solved utilizing basic properties of logarithms.
Step-by-step explanation:
To solve equations where a logarithm is equal to another logarithm, such as logz(2x - 3) = log2(x + 4), you can apply the property that if two logarithms (with the same base) are equal, then their arguments must also be equal. This means you can set the arguments equal to each other and solve for the variable: 2x - 3 = x + 4. Subtract x from both sides and add 3 to get x = 7.
To solve equations where a logarithm is equal to a number, such as log3(x - 1) = 2, you can use the property that the logarithm of a number is the exponent to which the base must be raised to get the number inside the log. This means you can convert the logarithmic equation to an exponential equation: 32 = x - 1. Solve for x by adding 1 to both sides to get x = 10.
The key properties of logarithms such as the product property, quotient property, and the power property are fundamental in solving various logarithmic equations.