Evaluate logarithms

Learning Objectives Define a logarithm as the inverse of an exponential function. Convert expressions between logarithmic form and exponential form. Evaluate logarithms with integer, fractional, or negative results without a calculator. Evaluate special logarithms, including log_b(1) and log_b(b). Apply the Change of Base formula to evaluate any logarithm using a calculator. Solve simple logarithmic equations by evaluating the logarithm. How many times more intense is a sound of 80 decibels than one of 50 decibels? 🤔 The answer lies in the power of logarithms! This tutorial will demystify logarithms by showing you they are simply a different way to think about exponents. You will learn the fundamental skill of evaluating logarithms, which is the key to solving exponential...

TermDefinitionExample LogarithmThe exponent to which a specified base must be raised to obtain a given number. It answers the question: 'What exponent do I need?'In the expression log₂(8) = 3, the logarithm is 3 because 2³ = 8. BaseThe number that is being raised to a power. In logarithmic form, it is the subscript number.In log₂(8), the base is 2. ArgumentThe number that you are taking the logarithm of.In log₂(8), the argument is 8. Logarithmic FormAn equation written in the form log_b(y) = x, where 'b' is the base, 'y' is the argument, and 'x' is the exponent.log₃(9) = 2 Exponential FormAn equation written in the form b^x = y, where 'b' is the base, 'x' is the exponent, and 'y' is the result.3² = 9 Common LogarithmA l...

Logarithm-Exponent Equivalence log_b(y) = x <=> b^x = y This is the most fundamental rule. Use it to convert between logarithmic and exponential forms to solve for an unknown value. Remember: the base of the log is the base of the exponent. Logarithmic Identity Rules 1. log_b(b) = 1 2. log_b(1) = 0 1. The logarithm of a number that is the same as the base is always 1 (since b¹ = b). 2. The logarithm of 1 is always 0 for any valid base (since b⁰ = 1). Change of Base Formula log_b(a) = log_c(a) / log_c(b) Use this formula to evaluate a logarithm with any base using a calculator, which typically only has buttons for base 10 (log) or base e (ln). You can choose any new base 'c', but 10 is the most common choice.