Certainly! Here are some common logarithmic formulas:

1. Change of Base Formula:

• log_b(x) = log_c(x) / log_c(b)
• This formula allows you to change the base of a logarithm to a different base by using logarithms with a known base.

1. Product Rule:

• log_b(x * y) = log_b(x) + log_b(y)
• When multiplying two numbers inside a logarithm with the same base, you can rewrite it as the sum of the logarithms of the individual numbers.

1. Quotient Rule:

• log_b(x / y) = log_b(x) – log_b(y)
• When dividing two numbers inside a logarithm with the same base, you can rewrite it as the difference of the logarithms of the individual numbers.

1. Power Rule:

• log_b(x^a) = a * log_b(x)
• When a number is raised to a power inside a logarithm, you can bring the exponent out as a coefficient in front of the logarithm.

1. Change of Base Formula for Natural Logarithm (ln):

• ln(x) = log_b(x) / log_b(e)
• Similar to the change of base formula, this formula allows you to express the natural logarithm (base e) in terms of logarithms with a different base.

1. Exponential and Logarithmic Equivalence:

• b^log_b(x) = x
• log_b(b^x) = x
• These formulas demonstrate the relationship between exponentiation and logarithms. If you raise a base b to the power of the logarithm of x to the base b, you obtain x, and vice versa.

These formulas can be useful for simplifying logarithmic expressions, solving equations involving logarithms, or converting logarithms between different bases.

It’s important to note that these formulas assume positive values for the bases and arguments of logarithms unless otherwise specified. Also, be cautious when working with logarithms of negative numbers or zero, as they may not be defined in some cases.

Remember to consult textbooks, mathematical references, or online resources for a more comprehensive list of logarithmic formulas and their applications in specific areas of mathematics and science.